Acme Mathematics 7

Acme Mathematics 7 101Exercise 2.171. Find the ratio of the following: (a) 200 to 75 (b) 84 m to 63 m (c) 18 km to 112 km (d) 300 ml to 6 liters(e) 3 days to 3 weeks (f) 800 paisa to 7 rupees 2. Compare the following ratios: (a) 3 : 5 and 4 : 7 (b) 4 : 5 and 8 : 10 (c) 5 : 9 and 7 : 11 (d) 10 : 35 and 230 : 120 (e) 213 : 3 and 49 : 245 (f) 113 : 213 and 313 : 4133. In a school, there are 260 students and out of them 182 are boys, find: (a) ratio of boys and girls, (b) ratio of girls and boys (c) ratio of boys and total students(d) ratio of girls and total students 4. (a) Divide 30 mangoes between two boys Ramji and Shyamji in the ratio of 2:3. (b) Divide Rs. 220 in the ratio 10:12.(c) Divide 270 kg in the ratio 5:45. (a) Two numbers are in the ratio 3:4. If their sum is 133, find the numbers. (b) The ratio of the number of boys and girls in a class is 8 : 7. If there are 60 students, find the number of boys and girls. 6. (a) The ages of mother and daughter are in the ratio 5 : 3. If the age of mother is 50 years, find the age of her daughter.(b) The ratio of length and breadth of a room is 5 : 3. If the room is 30 m long find the breadth of the room. 7. (a) The current ages of a father and his son are 40 years and 10 years respectively. What will be the ratio of their ages after 20 years? (b) Two numbers are in the ratio 2 : 3. when x is added on both part it is 7 : 8. Find the value of x.

102 Acme Mathematics 78. (a) The ratios of two numbers is 2 : 5. If the large number is 75, find the smaller number. (b) Two numbers are in the ratio 5 : 3. If the smaller number is 36, find the greater number. 9. Sunita sits for exam for three papers and gets the marks as follows:Subjects English Opt. Maths Comp. MathsFull Mark 80 100 50Mark Secured 64 90 44(a) Calculate the ratio of full marks of Opt. Maths and Comp. Maths. (b) Calculate the ratio of secured marks of English and Opt. Maths. (c) Calculate the ratio of secured marks of Opt. Maths and Comp. Maths. (d) In which subject performance is best?10. (a) Find the actual length and breadth of the given frame. When the ratio of its length in figure and actual length are in the ratio 1 cm : 8 cm.(b) The representative fraction of a map is 1 cm : 2500 km. The distance between two places A and B shown on the map is 12.5 cm. Calculate the actual distance between A and B.Project WorkCollect the number of boys and girls of your school and calculate the following:(a) The ratio between total number of boys to girls.(b) The ratio between number of boys and girls of class 7.(c) The ratio between total number of students and number of students of class 7.AB

Acme Mathematics 7 103C ProportionIn the earlier class, we learnt that ratios are used to compare quantities of the same unit. The ratio of Rs. 20 and Rs. 30 is 2:3 and ratio of Rs. 40 to Rs. 60 is also 2:3. Hence, Rs. 20:Rs.30:: Rs.40:Rs.60 and we say that four quantities are in proportion.The equality of two ratios is called proportionIf ab and cd are two ratios and ab = cd then a, b, c and d are called proportional. In a : b = c : d, a and d are called extremes and b and c are called means. The product of the extremes and the product of means are equal. 'a' is called the first proportional. 'b' is called the second proportional.'c' is called the third proportional. 'd' is called the fourth proportional.Solved ExampleExample 1 Test whether the ratios 4:6 and 8:12 are in proportion or not ? Solution: Here, given ratios are 4 : 6 and 8 : 12. Two ratios are in proportion, if the product of extremes = product of means Now, the product of extremes = 4 × 12 = 48 The product of means = 6 × 8 = 48 Here, product of extremes = product of means Hence, the ratios 4 : 6 and 8 : 12 are in proportion. Example 2 If 6, 9 and 24 are in proportion, find the fourth proportional. Solution: Let the fourth proportional = x then, 6, 9, 24 and x are in proportion So, 6 : 9 = 24 : x or, 69 = 24xor, 6x = 24 × 9 or, x = 24 × 96or, x = 36 Hence, the fourth proportional is 36.

104 Acme Mathematics 7Example 3 Binod bought 200 kg of rice for Rs. 4200. What is the cost of 51 kg of rice at the same rate? Solution: Let the required cost be Rs. x.Then 200 kg 51 kgRs. 4200 Rs. xThis problem is direct proportion So, 2004200 = 51xor, 200 x = 51 × 4200 or, x = 51 × 4200200or, x = 51 × 21or, x = 1071 Thus, 51 kg of rice cost Rs. 1071.Classwork1. Tick () the proportion.(a) 2 : 3::4 : 6 (b) 8 : 9 ::10 : 11(c) Rs 16 : Rs 32 :: Rs 2 : Re 1 (d) 2ft : 4 ft :: 6 ft : 8 ft2. Write the extremes and means in the following proportion.(a) 3 : 4 ::9 : 12 (b) 8 : 4 :: 2 : 1(c) 9 : 15 :: 3 : 5 (d) 3 ft : 8 ft :: 12 ft : 32 ft3. Prove that the following quantities are in proportion . (a) 3, 4, 9, 12 (b) 8, 24, 9, 27(c) 5, 7, 20, 28 (d) 4, 5, 12, 15(e) 6, 7, 18, 21 (f) 6, 5, 12, 10 4. Find which of the following quantities are in proportion. (a) 3, 4, 6, 8 (b) 15, 20, 25, 30 (c) 16, 64, 256, 512 (d) 40, 30, 8, 6(e) 300, 150, 30, 50 (f) 2.5, 5,10, 30

Acme Mathematics 7 105Exercise 2.181. Find the value of 'x' from the given proportion: (a) x : 4 :: 6 : 8 (b) 15 : x :: 10 : 12 (c) 1415 = x45(d) 20x = 100150 (e) 500 : 400 = 2500 : x (f) 99 : 45 = 44 : x 2. Following numbers are in proportion, find the value of x: (a) 3, 5, 6, x (b) 1, x, 5, 15 (c) x, 7, 2, 14 (d) 3, 7, x, 56 (e) 27, x, x, 3 (f) 4, x, x, 16 3. (a) 30, 50, 60 and x are in proportion, find the value of x. (b) 6, x, 36 and 12 are in proportion, find the value of x. 4. Find the value of 'b' in terms of 'a':(a) a : b = 6 : 8 (b) 8 : b = a : 9 (c) 7 : b = 4 : a 5. Find the value of a in terms of 'b': (a) a : b = 4 : 5 (b) b : a = 6 : 7 (c) 5 : b = a : 9 6. (a) Find the mean proportion between 27 and 3. (b) Find the mean proportion between 4 and 16. 7. (a) If the price of 10 pens is Rs. 400, how many pens can be bought for Rs. 480? (b) The cost of 7 kg of potato is Rs. 84. Find the cost of such 4 kg of potato. 8. (a) A man walks 4 km per hour. How long time will he take to walk 600 m?(b) A bus runs 40 km per hour. How long time will it take to run 900 m? 9. The ratio of length and breadth to a rectangle is 8:5. If its breadth is 15 m find: (a) Length of the rectangle (b) Area of rectangle (c) Perimeter of rectangle. 10. The ratio of length and breadth to a rectangle is 4 : 3. If its breadth is 12 m find: (a) Length of the rectangle (b) Area of rectangle (c) Perimeter of rectangle. 12 m11. The ratio of length and breadth to a rectangle is 9 : 7. If its length is 18 m find: (a) Breadth of the rectangle (b) Area of rectangle (c) Perimeter of rectangle.

106 Acme Mathematics 7EvaluationTime: 50 minutes Full Marks: 211. Out of 40 students of class 7, 15 of them like English, 25 like mathematics and reminder students like science. (a) Find the number of students who likes Mathematics and English ? [2](b) Find the number of students who does not like both ? [2](c) What is the multiplicative inverse of 127. [1](d) Simplify: 23.78 – 2.375 + 8.2 [1]2. Ramesh is a teacher of a school. He has spend 12 part of his income in food and 14 part of his income in education. (a) In which title between food and education will he spent more ? [1](b) He has monthly income Rs. 30,000. What is his monthly saving ? [2](c) Write any two rational numbers between 12 and 14. [2](d) Which number is added to the 12 so that sum is equal to 14 ? [1]3. Pramod’s height is 165 cm. and Pramila’s height is150 cm. (a) Find the ratio of Pramod and Pramila height. [1] (b) Find ratio of Pramila and Pramod height. [1] (c) Simplify: 34 + 56 − 112 [2](d) Which number is subtracted to the numerator and denominator of 29 so that difference is equal to 43 ? Calculate it. [1]4. In a school, 13 part of total student were girls. The number of girls is 140. (a) Find the total number of students. [1] (b) Find the total number of boys. [1] (c) Find any two rational numbers between 14 and 12. [2]

Acme Mathematics 7 1072.6 Profit and Loss1. If selling price = SP, Cost Price = CP, profit = P and Loss = L, fill in the blanks: (a) SP – CP = ................ (b) CP – SP = ................ (c) Profit = .................... (d) Loss = ..................... 2. Fill in the blanks, when.(a) CP = Rs. 40 and SP = Rs. 50 then, profit =................. (b) CP = Rs. 6 and profit = Rs. 2 then, SP =................. (c) CP = Rs. 12 and loss = Rs. 4 then, SP =.................(d) SP = Rs. 10 and CP = Rs. 15 then, loss =............... 3. Find the CP, when its SP = Rs. 100 and loss = Rs. 30 4. A table is made at a cost of Rs. 800, what is the profit, if it is sold for Rs. 1000? 5. Robin bought 5 apples for Rs. 50 and sold each apple at the rate of Rs. 12, what did he gain? 6. Sabin bought 1 dozen pen at the rate of Rs. 35 per pen and sold at the rate of Rs. 40 per pen. Find his total profit. 7. Six pens are bought for Rs. 180 and sold for Rs. 35 each. Find the total profit.8. Nabin bought 6 quintals of sugar at the rate of Rs. 75 per kg and sold at the rate of Rs. 74 per kg, find his loss. 9. The selling price of a TV is Rs. 12500 and loss is Rs. 600 find the cost price of the TV. 10. If loss is Rs. 200 and cost price Rs. 900, find its selling price. 11. Ram bought a radio for Rs. 1550 and sold it at a profit of Rs. 315, find its selling price.Warm Up TestA RevisionWe have already learnt about profit and loss. If the selling price (S.P.) is more than itscost price (C.P.), we say that there is a profit or gain. Similarly, if the selling price (S.P.)is less than its cost price (C.P.), we say that there is loss. In short: If S.P. > C.P then there is profit so, profit(P) = S.P. – C.P.If C.P. > S.P. then there is loss so, loss (L) = C.P. – S.P.,

108 Acme Mathematics 7Solved ExampleExample 1 Sanju bought a book for Rs. 165 and sold it for Rs. 170. Find her profit. Solution: Selling price of a book (S.P.) = Rs. 170 Cost price of a book (C.P.) = Rs. 165 Since, S.P. > C.P., there is profit Therefore, Profit = S.P. – C.P. = Rs. 170 – Rs. 165= Rs. 5. Hence, her profit is Rs. 5. Example 2 A dealer bought a calculator for Rs. 660 and sold it for Rs. 606, find his loss. Solution: Selling price of the calculator (S.P.) = Rs. 606 Cost price of the calculator (C.P.) = Rs. 660 Since, S.P is less than C.P., there is loss Therefore, Loss = C.P. – S.P. = Rs. 660 – Rs. 606 = Rs. 54 Hence, his loss is Rs. 54.Classwork1. Find the profit or loss: (a) Cost Price = Rs. 1200, Selling Price = Rs. 1500 (b) Cost Price = Rs. 600, Selling Price = Rs. 800 (c) Cost Price = Rs. 1500, Selling Price = Rs. 1800 (d) Cost Price = Rs. 2000, Selling Price = Rs. 1600 (e) Cost Price = Rs. 2500, Selling Price = Rs. 2450 (f) Cost Price = Rs. 900, Selling Price = Rs. 890 Exercise 2.191. Find C.P. in each of the following conditions: (a) Selling Price = Rs. 1200, Profit = Rs. 400 (b) Selling Price = Rs. 1550, Profit = Rs. 350 (c) Selling Price = Rs. 2100, Profit = Rs. 500

Acme Mathematics 7 109(d) Selling Price = Rs. 1800, Profit = Rs. 300 (e) Selling Price = Rs. 2500, Profit = Rs. 800 (f) Selling Price = Rs. 3000, Profit = Rs. 450 2. Find S.P. in each of the following conditions: (a) Cost Price = Rs. 4000, Profit = Rs. 800(b) Cost Price = Rs. 3000, Profit = Rs. 1200(c) Cost Price = Rs. 2500, Profit = Rs. 900 (d) Cost Price = Rs. 2000, Loss = Rs. 600 (e) Cost Price = Rs. 3500, Loss = Rs. 400 (f) Cost Price = Rs. 5000, Loss = Rs. 1000 3. Sansar bought 6 oranges for Rs. 30 and sold each orange at Rs. 6. What did he gain? 4. Navin bought 1 dozen pens at the rate of Rs. 35 per piece and sold at the rate of Rs. 38 per pen. Find his total profit. 5. Samar bought 5 quintals of sugar at the rate of Rs. 32 per kg and sold it at the rate of Rs. 31.50, find his loss. 6. A fruit seller buys 144 oranges for Rs. 576. If his profit is Rs. 288, find the selling price of each orange. 7. By selling 12 tables for Rs. 14,400, Balram loses Rs. 2880. Find the cost price of each table.B Percentage of Profit and LossSuppose a dealer buys a fan at the rate of Rs. 1450. He sells it for Rs. 1696.50 and makes a profit of Rs. (1696.50 – 1450) = Rs. 246.50. The profit or loss is always measure on the initial cost price, it is customary to express profit or loss as a percent of the cost price. In the above example, by selling the fan for Rs. 1696.50, the dealer makes a gain of 246.501450 × 100% = 17% If the dealer sells it for Rs. 1377.50, he suffers a loss of 72.51450 × 100% = 5%. Thus, we derive the following formulae for profit and loss percentage. (i) Profit percent = ProfitCost price × 100% = SP – CPCP × 100% (ii) Loss percent = LossCost price × 100% = CP – SPCP × 100%

110 Acme Mathematics 7Solved ExampleExample 1 Find the percentage of profit when CP = Rs. 500 and SP = Rs. 550. Solution: Cost price (CP) = Rs. 500 Selling price (SP) = Rs. 550 We know that, Profit percentage = SP – CPCP × 100% = Rs. (550 – 500)Rs. 500 × 100% = Rs. 50Rs. 500 × 100% = 10% ∴ The profit percentage is 10%.Example 2 Kashi bought a second hand computer for Rs. 12,000 and spent Rs. 2,000 on its repair. He sold it for Rs. 13,000. Find his loss percent. Solution: Cost price (C.P.) = Rs. 12,000 Repairing cost = Rs. 2,000 ∴ Total cost price = Rs. 12,000 + Rs. 2,000 = Rs. 14,000 Selling Price = Rs. 13,000 We know that, Loss percent = CP – SPCP × 100% = Rs. (14000 – 13000)Rs. 14000 × 100% = 100014000 × 100% = 717 %∴ The loss percentage is 717 %.Classwork1. Write the full form:(a) S.P. (b) C.P.2. Write true or false for the following statements:(a) Profit is made when CP > SP.(b) Loss is made when SP < CP.

Acme Mathematics 7 111(c) Neither profit nor loss is made when CP = SP.(d) Loss is calculated by SP – CP.(e) Profit is calculated by CP – SP.(f) Profit percentage = ProfitCost price × 100%3. Find the gain percent in the followings: (a) Cost Price = Rs. 140, Selling Price = Rs. 145 (b) Cost Price = Rs. 402, Selling Price = Rs. 502 (c) Cost Price = Rs. 120, Selling Price = Rs. 1444. Find the loss percent in the followings: (a) Cost Price = Rs. 370, Selling Price = Rs. 350(b) Cost Price = Rs. 3000, Selling Price = Rs. 2850 (c) Cost Price = Rs. 28000, Selling Price = Rs. 26000 Exercise 2.201. Find the gain percent in the followings: (a) Cost Price = Rs. 432, Selling Price = Rs. 543 (b) Cost Price = Rs. 250, Selling Price = Rs. 260 (c) Cost Price = Rs. 900, Selling Price = Rs. 1000 2. Find the loss percent in the followings: (a) Cost Price = Rs. 240, Selling Price = Rs. 124 (b) Cost Price = Rs. 500, Selling Price = Rs. 450 (c) Cost Price = Rs. 900, Selling Price = Rs. 890 3. Find the gain percent or loss percent in the followings: Selling price (Rs.) Gain (Rs.) Loss (Rs.)(a) 6000 100 – (b) 248 – 22 (c) 450 50 – (d) 90 – 10 4. Find the cost price when, (a) Selling price = Rs. 725 and 15% gain (b) Selling price = Rs. 5000 and 25% loss.

112 Acme Mathematics 75. Find the selling price when,(a) Cost price = Rs. 250 and 5% gain (b) Cost price = Rs. 2300 and 10% loss (c) C.P. = Rs. 25 and profit = 10% (d) C.P. = Rs. 100 and profit = 5% (e) C.P. = Rs. 500 and loss = 8 %(f) C.P. = Rs. 1250 and loss = 7%6. If an article bought for Rs. 270 is sold for Rs. 324, what is the profit percent? 7. Ramesh bought a car for Rs. 7,00,000 and sold it for Rs. 6,75,000; find his loss percent. 8. Ranjit bought a motorbike for Rs. 82,500. Due to some defects in it, he had to pay Rs. 1250 for repair. Then, he sold it for Rs. 85,000, find his gain percent.9. Bishnu sold a cow at a profit of 20% with selling price Rs. 850. Find the cost price of the cow. 10. Sujan sold a watch for Rs. 785 at a loss of 5%, find its cost price. 11. An article bought for Rs. 250 is sold at a profit of 20%. What is the selling price? 12. An article bought for Rs. 500 is sold at a loss of 15%. What is the selling price? 13. A calculator is sold for Rs. 230 at a profit of 15%.(a) What is its cost price? (b) At what price must it be sold to make a profit of 10%? 14. A watch is sold for Rs. 1700 at a loss of 10%, (a) What is its cost price? (b) At what price should it be sold to gain 20% ? 15. 120 eggs are bought at Rs. 108 per dozen and sold at Rs. 12 per egg. Calculate profit percent or loss percent.Project WorkCollect the price of four different goods from three different shop and choose the shop to buy the goods.

Acme Mathematics 7 1132.7 Unitary Method1. Look at the following price list:Rs. 450 Rs. 280 Rs. 23 Rs. 30Now complete the given table:Goods Cost of 1 unit Cost of 3 units Cost of 5 units Cost of 100 unitsBagCopyPenGeo-box2. Fill in the blanks.Unit cost 2 units cost 3 units cost 4 units cost 5 units costRs. 5 .................... 15 .................... Rs. 25.................... Rs. 8 .................... Rs. 16 ....................3. Complete the table.2 Unit cost units cost 3 units cost Rs. 30 ............................ ............................Rs. 40 ............................ ............................4. Working days and number of men are given in the table. Remember the inverse relation and complete the table.Working days 40 .................... 20 ....................Number of workers 10 20 .................... 85. Identify the direct variation problems. (a) Problems related to number of pen and its cost. (b) Problems related to number of worker and working days. (c) Problems related to number of men and their eyes. Warm Up Test

114 Acme Mathematics 7A Direct variationYou already studied ratio, proportion and unitary method in previous classes. In this class, we shall use the concept of proportion and unitary method to develop the concept of variation. Study the following table:Weight of sugar (in kg) (x) 5 10 15 20 25 30 35Cost of sugar in Rs. (y) 150 300 450 600 750 900 1050The graph of above information is given alongside. Now, examine the table and graph and try to answer the following questions. (i) What is the amount of sugar (in kg) costing Rs 450? (ii) What is the cost of 30 kg of sugar? (iii) What is the relation between the weight and the cost of sugar?In the table above, we see that when the value of x increases the value of y also increases. But the ratio xy for various values of x and y are same (constant) i.e. 5150 = 10300 = 15450 and so on. Hence, the above relation shows that x and y increase or decrease together. If we increase the value of either variable (x or y), then we must suitably increase the value of the other variable. Similarly, if we decrease the value of either variable (x and y) we must suitably decrease the value of the other variable. In such a case, we say that x and y vary directly to each other. Thus, two quantities x and y are said to vary directly to each other, if they increase or decrease together in such a manner that the ratio of their corresponding values remain constant.Solved ExampleExample 1 The cost of 10 meters of cloth is Rs. 300. Answer the followings question with the help of graph given below. (a) What is the cost of 5 meters of cloth? (b) How much meters of cloth can be bought in Rs. 450?Solution: (a) The intersection of line through 5 meters and Rs 150 is the point A. ∴ The cost of 5 meters of cloth is Rs 150. (b) Similarly, 15 meters of cloth can be bought for Rs 450. O X' XY' Weight of sugar (x) in kgCost of sugar (y) in Rs.Y51200600900300105045075015010 15 20 25 30 35 40O X' XY' Cloth in metre (x)Cost of cloth (y)Y5A60090030045075015010 15 20 25 30

Acme Mathematics 7 115Example 2 A car travels 432 km on 54 litres of petrol. How far does it travel on 25 litres of petrol? Solution: On 54 litres of petrol, a car travels 432 km On 1 litre of petrol, a car travels 43254 km On 25 litres of petrol, a car travels 432 × 2554 = 200 km. Therefore, on 25 litres of petrol a car travels 200 km. Example 3 If the cost of 5 kg of tomatoes is Rs 50. What will be the cost of 95 kg of tomatoes? Solution: Let the required cost be Rs x.Tomato (kg) Cost (Rs.)5 5095 xThis is the case of direct variation; so the ratio of amount of tomato will be equal to the ratio of price. Therefore, 595 = 50x or, 5x = 50 × 95or, x = 50 × 955or, x = 950 Thus, the price of 95 kg of tomato is Rs 950.Classwork1. If 10 marbles cost Rs 5, what is the price of 24 such marbles? 2. The price of 3 books is Rs 330. How many such books can be bought for Rs 550? 3. The cost of 25 litres of petrol is Rs 4000. Find the cost of 30 litres of petrol. 4. If 24 notebooks costs Rs. 288, what is the cost of 10 notebooks? 5. If a car travels 700 km in 12 hours, in how many hours will it travel 600 km? 6. The weight of 35 bags of rice is 1750 kg. How many such bags will weigh 850 kg? 7. An electric pole of height 25 m casts a shadow of 20 m. Find the height of a tree, if it casts a shadow of 12 m under similar conditions. 8. A worker is paid Rs. 450 for 6 days of work. If his total income for the same type of work is Rs 1800, for how many days did he work?

116 Acme Mathematics 79. Complete the table:Goods Estimated Cost Cost of 2 goods Cost of 5 goodsExercise 2.211. 50 kg of tomatoes cost Rs. 2500. Find the cost of 13 kg of the same type of tomatoes. 2. A car can cover a distance of 702 km on 39 litre of petrol. How much distance will be covered by the car with 29 litre of petrol? 3. Bishnu types 1800 words in half an hour. How many words will he type in 16 minutes? 4. Meera types 720 words during 45 minutes. How many words does she type in 1 hour? 5. If the cost of 47 m cloth is Rs 1175 , what length of the same cloth can be purchased by Rs. 800? 6. A private taxi charges a fare of Rs. 2400 for 300 km of journey. Find the distance to be covered by the taxi for Rs 2800? 7. The time of tailoring of 2 shirts is 5 hours. What is the time of tailoring of 5 such shirts?

Acme Mathematics 7 1178. A bus covers 95 km in 114 hours, find the time required to cover a distance of 266 km, if the speed is same. 9. An agent received a commission of Rs 25 on sales of Rs 100. How much commission will he get on the sales of Rs 1,50,000? 10. Replace each '?' in the following table by suitable number if x and y are in direct variation:x 2 7 ? 60 ? 1.5 ?y 6 21 45 ? 90 ? ?11. Rs 5000 is the expenditure of a family of 5 persons for 30 days. For how long will Rs 7500 support the same family?12. 12 men can earn Rs 6000 in a week. By how many men can Rs 9000 be earned in the same time?13. The exchange rate of Nepalese currency (NC) and Indian currency (IC) is given below: [ N. C. Rs. 160 = I. C. Rs.100] Answer the following questions: (a) How much IC can be exchanged for Rs 7000 NC? (b) How much Nepalese rupees can be exchanged for Rs 2000 IC? (c) Express the relation in equation from. 14. A dealer bought 23 motorcycles for Rs 2194200. How much would he pay for 35 such motorcycles? 15. Draw the graph of given information:Apple (kg) 2 1 3 4 5 6 7 8Cost (Rs.) 80 40 120 160 200 240 280 320

118 Acme Mathematics 7B Indirect VariationStudy the following table:Number of persons (x) 1 2 4 5 10 20Days required to complete the work (y) 20 10 5 4 2 1The graph of above information is shown below. Now examine the table or graph and try to answer the following questions: (a) How many days are required to complete a work by 2 men? (b) How many days are required to complete a work by 10 men? (c) How many men are needed to complete a work in 4 days? (d) How many men are needed to complete a work in 5 days? (e) What is the relation between the men and the days? From the table or graph above, we see that as the value of x increases, the value of y decreases and vice versa. The ratios of xy for various values of x and y are not same in case of this variation. This is indirect (inverse) variation. Therefore, two quantities are said to be in inverse variation, if one increases makes the other decreases or vice versa.Solved ExampleExample 1 A car can complete a certain distance in 15 hours at the speed of 60 kilometres per hour. By how much should its speed be increased so that it may take only 12 hours to cover the same distance?Solution: Let the required speed of a car is x km/hrs.Time (hours) Speed (km)15 6012 xThis is case of indirect variation, So, we have, 1512 = x60or, 12x = 60 × 15 or, x = 60 × 1512 ∴ x = 75 Thus, the required increase in speed = (75 – 60) km/hrs = 15 km/hrO X' XY' Number of persons (x)Number of days (y)Y21482041610618122 4 6 8 10 12 14 16 18 20

Acme Mathematics 7 119Example 2 If 30 men can do a work in 40 days, then in how many days 15 men will complete the same work? Solution: Here, given information areMen Days30 4015 x (let)(a) Indirect variation method: Let, the required days = x , This is indirect variation. So, we have, x40 = 3015or, x = 30 × 4015 or, x = 80 Thus, 15 men will complete the same work in 80 days. (b) Unitary method: 30 men can do a work in 40 days. 1 man can do a work in 40 × 30 days 15 men can do a work in 40 × 3015 days = 80 days ∴ 15 men will complete the same work in 80 days. Example 3 A can do a piece of work in 10 days and B can do the same work in 12 days. Find: (a) Work of A, in 1 day. (b) Work of B, in 1 day. (c) Work of A and B, in 1 day. (d) The number of days to finish the work, if they work together.Solution: Here, A can do a work in 10 days. B can do a work in 12 days. Now, (a) This problem in indirect variation. In 10 days A can complete 1 work.In 1 day, A can complete 110 work. Hence, A can do 110 of the work in 1 day. (b) In 12 days B can complete 1 work. In 1 day B can complete 112 work. Hence, B can do 112 of the work in 1 day.

120 Acme Mathematics 7(c) Work of A and B in 1 day = ( 110 + 112 ) of the work = 6 + 560 = 1160 of the work. (d) 1160 of the work can finished by (A + B) in 1 day. 1 work can finished by (A + B) in 6011 days = 5 511 days Hence, if they work together they will finish the work in 5 511 daysClasswork1. Tick () the correct statements.(a) If the number of pencils increase, their total cost also increases.(b) In case of direct variation, more value is obtained by multiplying the unit value by given quantity.(c) In case of inverse variation more value is obtained by multiplying the unit value by given quantity.(d) If the number of worker decreases time taken to complete the work also decreases.2. If 6 men can do a piece of work in 8 days, in how many days 3 men take to do it? 3. If 30 men can do a piece of work in 8 days, how many men can do the same work in 12 days? 4. In how many days can 40 men do a piece of work, if 20 men can do the same work in 40 days? 5. A school's hostel has enough food for 500 children for 18 days. How long will the food last, if 100 more children join them? Exercise 2.221. 18 pumps can empty a tank in 6 hours. In how many hours can 30 pumps do the same work? 2. 40 workers can complete the construction of a building in 36 days. How many workers are needed to construct the same building in 12 days? 3. If 75 cows can graze a field in 20 days, How many such cows will graze the field in 30 days? 4. 400 people have a stock of food for 9 weeks. How long will the same stock last for 300 such people? 5. A fort has enough food for 500 soldiers for 32 days. How long will the food last for 450 soldiers? 6. A garrison of 400 men had food for 40 days. 200 more men joined them. How long will the food last now?

Acme Mathematics 7 1217. A bridge can be constructed by 1500 workers in 60 days. How many workers should be employed to complete the work in 40 days? 8. 5 farmers can cultivate a land in 8 days. How many farmers should be engaged so as to complete the work in 4 days? 9. 20 taps can empty a reservoir in 10 hours. In how many hours does 40 such taps take to empty the same reservoir?10. A journey takes 3 hours 30 minutes at the speed of 40 km per hour. How long would it take if the speed were 60 km per hour? 11. Draw the graph of given information:Number of hours 5 10 15 20 25 32 40Speed (km/hr) 40 20 13.33 10 8 6.25 512. Speed and time taken to travel a distance of 500 km for a bus are given below. Copy and complete the table.Speed (km/hr) 10 ? 25 40 ? 60 75 80 ?Time (hour) 50 25 ? 12.5 10 813 ? 614 513. (a) 5 women can complete a piece of work in 24 days. How many women can complete the same work in 12 days? (b) 200 laborers need 50 days to construct a road. How many laborers is needed to construct the road in 80 days? (c) 10 workers are required to complete a work in 20 days. How many workers are required to complete the same work in 10 days? (d) 16 men can reap 20 'Bighas' field in 12 days. How long will it take for 18 men to reap the same field? (e) 30 men can load a truck of goods in 4 hours. How long will it take for: (i) 12 men (ii) 40 men to load the same amount of goods?

122 Acme Mathematics 71. (a) What is square number? (b) Find the cube number of 7.(c) Find the square root of 9801 by division method.2. (a) Write, how we find HCF and LCM ?(b) Find the HCF of 100, 125 and 200 by prime factor method.(c) Find the smallest number which is divisible by 24, 36 and 56.3. (a) Find the square number of 10. (b) Find the cube number of 6.(c) Find the prime factors of 30.4. (a) Find the square root of 144. (b) Find the HCF: 36, 48, 72(c) Find the smallest number which can be divided by 12, 18, and 24 with out remainder.5. A square field has length of 9 m. 625 cauliflowers were planted in the field as a square row.(a) What is the area of the square field?(b) How many cauliflowers were planted on one row?(c) A cube has volume 216 cm3. Find its length.(d) Write any two numbers which is both a square and a cube number.6. Hari Krishna went to a temple and heard three bells ringing together. They ring at the interval of 12 minutes, 16 minutes and 24 minutes respectively.(a) After what interval of time will they again ring together?(b) If it was 7:00 AM. At what time they would ring togeter for the 2nd time?(c) If each mobile set is 12 cm long, 6 cm broad and 1 cm thick, find the ratio of its length to the breadth.7. There are 3600 samosa, 720 packets of noodles and 1680 packets of biscuits.(a) Find the greatest number of students that can be distributed equally.(b) Calculate the share of each item for a student(c) Express the number of samosa in square form.(d) Is the packets of biscuits a cube number?Mixed Exercise

Acme Mathematics 7 1238. (a) Define rational number.(b) Simplify: 325 – 2 710 + 115 (c) Find the product of 213 and 338.9. Following are some numbers.21 22 23 24 25 26 27 28 29 3031 32 33 34 35 36 37 38 39 4041 42 43 44 45 46 47 48 49 5051 52 53 54 55 56 57 58 59 6061 62 63 64 65 66 67 68 69 70(a) Indentify the cube numbers from the list.(b) Select the square numbers from the list.(c) Find HCF of 22 and 33.(d) HCF and LCM of two numbers are 14 and 168 respectively. If one number is 56, find the other.10. (a) Add the following integer by using number line. (+3) + (+4)(b) Divide: (+ 3) ÷ (+ 6)(c) Simplify: (+ 12) + ( – 5) + (+ 25) ÷ (– 5) – (– 6) × (+ 7)11. (a) Multiply: (+ 3) × (– 5) × (– 4). (c) Fill in the box: (+ 20) ÷ (– 4) = (b) Simplify: [(+ 6) × (+ 2)] ÷ [(– 3) × ( – 2)]12. (a) The integer which is 4 units right to [–1] is ......... (b) In a school Auditorium, there are three types of rows arrangements possible for watching a program: rows of 30 students in each row or rows of 40 students in each row or rows of 45 students in each row. What is the least number of students so that all the students can be accommodated in each of these arrangements?(c) There is a cubical reservoir water tank in Anamika's house. If the volume of the tank is 512 cubic meter, find the height of the tank.13. (a) Write the additive inverse of (+4).(b) The product of two number is (– 40). If one of them is (– 4), find the other.(c) Find the fraction equivalent to 0.22.14. Do the following.(a) The sum of two integer is – 87 and the greater integer 127, then what is the smaller integer?(b) The volume of a cubical box is 216 cm3. Find the length of its one side.(c) Which is greater 34 and 57 ?

124 Acme Mathematics 715. There are 15 students in class 7 who need to school shirt of same size and 213 meter of cloth is required to make a shirt.(a) Find the total length of the cloth required to make the shirt to them.(b) How many shirts can be made from a piece of cloth 913 meter long?(c) Convert the length of cloth required for a shirt in decimal.(d) If the length of a piece of cloth is 36.25 meter, how many meters of cloth is left?16. In a school there are 260 students and out of them 192 are boys. Find,(a) Ratio of boys and girls.(b) Ratio of girls and boys.(c) Ratio of boys and total students.(d) Ratio of girls and total students.17. Mother divided some money among Runa, Sama and Maria in the ratio of 2:3:5. Maria got Rs. 150.(a) Calculate the money received by Runa and Sama.(b) Find the total amount.(c) Simplify: 625 ÷ 910 – 728 × 42118. (a) Find the profit of cost price = Rs. 1200, selling price = Rs. 1500.(b) If the cost of 10 marbles is Rs. 5. What is the cost of 24 such marbles.(c) Find the cube root of 216.19. A shopkeeper sold 20 mobile sets of same brand for Rs. 3,000,00 at the same rate in a week.(a) What is the selling price of each mobile set?(b) If he bought each mobile set for Rs. 12,500, find his profit or loss percent.(c) If each mobile set is 12 cm long, 6 cm broad and 1 cm thick, find the ratio of its length to the height.20. Do the following.(a) Change in to percentage : 35(b) Shankar bought two dozen of notebooks at Rs. 1320. Find the cost of a notebook.(c) Rabin buys an old scooter for Rs. 47000 and spent Rs. 8000 on its repairs. If he sells the scooter for Rs. 58000. Find his profit or loss amount.

Acme Mathematics 7 12521. (a) There are 21 apples, 28 pears and 49 oranges. These are to be arranged in heaps containing the same number of fruits.(i) Find the greatest number of fruits possible to keep in each heap.(ii) How many heaps are formed by this arrangement?(b) If three buckets of capacities 10 l, 12 l, and 15 l can fill a drum in exact number of fillings. Find the least capacity of the drum.22. The two vehicles started their journey from Bharatpur. One vehicle travelled 120 km to the East and another vehicles travelled 200 km to the west.(a) Mark the two vehicles as A and B on a number line.(b) Find the distance between the vehicles.23. Do the following.(a) Define HCF.(b) Find the greatest number that exactly divides 240 and 336.(c) If 30 men can do a work in 40 days, then in how many days 15 men will complete the same work.(d) Convert the fraction 3454 into decimal number.24. The ratio of length and breadth of a rectangle is 9:7. Its length is 18 m.(a) Find breadth of the rectangle.(b) Find area of rectangle.(c) Find the third proportion of 8 and 12.25. Do the following.(a) Express the decimal 2.36 into fraction.(b) A watch is brought for Rs. 245 and is sold for Rs. 420. Find the profit or loss percentage.26. (a) A water tank has two pipes of different sizes to fill the tank. One pipe can fill 25parts of the tank and another pipe can fill 38 parts of the tank in 1 hours.(i) What parts of the tank would be filled in 1 hour if both the pipers are opened once?(ii) Which pipe would full the tank faster?(b) There are 40 students in a class and 16 of them are girls.(i) Find the ratio of the girls and the total number of students.(ii) Find the ratio of the girls and the boys.

126 Acme Mathematics 727. (a) Subtract : (+15) – (–3)(b) Find cubic root of 216.(c) Find HCF of 84 and 108.28. From an 11 m long rope, two pieces of lengths 135 m and 155 m are cut off.(a) Find the length of cutting parts of rope.(b) Find the length of the remaining part of the rope.(c) What is the length of the half of the remaining rope.29. Ram bought a book for Rs. 400 and sold at Rs. 350.(a) Find the ratio of cost price and selling price.(b) At what price should he sell it to gain Rs. 50.(c) Find the loss.30. Ram, Shyam and Hari are three brothers and their ages are 8 years, 16 years and 25 years.(a) What is HCF?(b) Find the HCF of their ages.(c) Find out the square number and cube number from their ages.31. Ramesh is a teacher of a school. He has spend 12 part of his income in food and 14 part of his income in education.(a) In which title between food and education will he spent more?(b) He has monthly income Rs. 30,000. What is his monthly saving?(c) Write any two rational numbers between 12 and 14.32. (a) Find the integer which is multiplied by (– 12) gives the product (+ 36)(b) Define rational number.(c) Simplify : 213 ÷ 56 – 13(d) When Rs. 32.5 is subtracted from Rs. 100, find out the amount of money left?33. Rakes bought a radio for Rs. 8000 and sold it for Rs. 8400,(a) What is the formula to find profit, if cost price and selling price are given?(b) Find out profit amount obtained by Rakes(c) Find the profit percentage.

Acme Mathematics 7 127EvaluationTime: 41 minutes Full Marks: 171. (a) Write the formula to find the profit percent. [1](b) Hariman bought a second-hand computer for Rs.15,500 and spent Rs.4,500 on its repair. At what price must the computer be sold to make profit of 4%? [2](c) When 15 pens are sold on Rs.1500 there is Rs 45 loss. Find the cost price of one pen. [1] 2. Rajeeb bought a table for 2400 rupees and sold it at a profit 20%.(a) Find the selling price when cost price and loss is given. [1] (b) Find the actual profit of table. [1] (c) Find the profit percentage of the table when it is sold at Rs. 2640. [2]3. Ramesh Sharma is stationer. He bought 20 books for Rs. 6000.(a) What is the cost price of 1 book. [1] (b) If he made a profit of Rs. 500, What is the selling price of the books ? [2](c) What is the selling price of a book ? [1] 4. A stationary shopkeeper bought 1 dozen of copies at Rs. 50 per piece and sold at Rs. 60 per piece.(a) Find the cost price of shopkeeper. [1] (b) How much money of profit or Loss does Shopkeeper make? [1] (c) Find his profit or Loss percentage. [2](d) How much he should pay if he bought only 20 copies? [1]

128 Acme Mathematics 73UNIT Mensuration1. Write the perimeter: (each room is 1 cm2)(a) (b) (c)P = .......... cm P = .......... cm P = .......... cm(d) (e) (f)P = ........ cm P = ........ cm P = ........ cm2. Write the perimeter of following figure.: (take base only)(a) (b) (c)P = .......... cm P = .......... cm P = .......... cm3. Find the perimeter of the following shapes.(a)2 cm1 cm2 cm(b)1 cm2.5 cm1.5 cm2 cm(c)3 cm2.5 cm1.5 cm 2 cm1 cm1 cmWarm Up Test

Acme Mathematics 7 1293.1 Perimeter of plane figures A. Perimeter of trianglePerimeter is a total length of the close figure. To find the perimeter of triangle we add the total length of its sides. Here, triangle ABC is a close figure;Now,Perimeter of triangle ABC = Sum of length of all sides= AB + BC + CA = (c + a + b) unitsB. Perimeter of quadrilateralPerimeter of quadrilateral is the sum of its all sides.To find the perimeter of quadrilateral, we add the total length of its sides. Here, quadrilateral ABCD is a close figure;Now,Perimeter of quadrilateral ABCD = Sum of length of all sides= AB + BC + CD + DAC. Perimeter of pentagonTo find the perimeter of pentagon, we add the total length of its sides. Here, pentagon ABCDE is a close figure;Now,Perimeter of pentagon ABCDE = AB + BC + CD + DE + EAThus, perimeter of any closed figure is the sum of length of all sides.D. Perimeter of a rectangleThe total length of the boarder of any plane figure is called its perimeter.Perimeter of a rectangular in terms of length (l) and breadth (b).Consider the given rectangle ABCD.Now, Perimeter of rectangle ABCD.= AB + BC + CD + DA= length + breadth + length + breadth= 2 length + 2 breadth= 2 (length + breadth)= 2 (l + b)Thus, the perimeter of a rectangle = 2 (l + b)ca bA BCABD CAB CDED lengthA BClengthbreadth breadth

130 Acme Mathematics 7E. Perimeter of a squareIn the figure, PQRS is a square. Its sides are PQ, QR, RS and SP. PQ = QR = RS = SPLet, Length of each side is 'l'.Now,Perimeter of square PQRS= PQ + QR + RS + SP= l + l + l + l = 4 lThus, the perimeter of a square = 4 lSolved ExampleExample 1 Find out the perimeter of the given triangle.Solution : Here, Length of three sides are 3 cm, 4 cm and 5 cmPerimeter = sum of three sides.= 3 cm + 4 cm + 5 cm= 12 cmHence, perimeter is 12 cm.Example 2 Find the length of the side BC of the triangle ABC.Solution : Here, perimeter = 16 cm, givenPerimeter of triangle = AB + BC + CAor, 16 cm = 6 cm + BC + 3 cmor, 16 cm = 9 cm + BCor, 7 cm = BCHence, length of the side BC is 7 cm.Example 3 Find out the perimeter of the given pentagon.Solution : Here, length of five sides are 4 cm, 3 cm, 3 cm, 3 cm, 5 cm.Now, Perimeter of pentagon = sum of five sides.= AB + BC + CD + DE + EA= 4 cm + 3 cm + 3 cm + 3 cm + 5 cm= 18 cmPerimeter is 18 cm.= ===SP QRll3 cm4 cm5 cmA BP = 16 cmC3 cm 6 cmAB CDE3 cm3 cm5 cm3 cm4 cm

Acme Mathematics 7 131Example 4 Find the perimeter of the given photo frame.Solution : Here, Photo frame is rectangular.Let, Length of frame (l) = 15 cmBreadth of frame (b) = 10 cmPerimeter = 2 (l + b)= 2 (15 cm + 10 cm)= 2 × 25 cm= 50 cmPerimeter of photo frame is 50 cm.Example 5 Find the perimeter of the square notice board.Solution : Here, Length of notice board (l) = 75 cmPerimeter = 4l= 4 × 75 cm = 300 cmPerimeter is 300 cm.Example 6 A rectangular A4 sized paper has length 11.7 inch and breadth 8.3 inch. Find its perimeter.Solution : Here, Length of paper (l) = 11.7 inchBreadth of paper (b) = 8.3 inchNow, Perimeter of rectangular piece of paper= 2 (l + b)= 2 (11.7 inch + 8.3 inch)= 2 × 20 inch = 40 inchPerimeter of a paper is 40 inch.Example 7 A rectangular park is 700 m long and 300 m wide. Find the distance covered by a man around it in 10 rounds.Solution : Here, Total distance = 10 × perimeter of the park.Length of park (l) = 700 mBreadth of park (b) = 300 mPerimeter = 2 (l + b)= 2 (700 m + 300 m) = 2 × 1000 m = 2000 m = 2 km10 cm15 cm75 cm75 cm75 cm75 cm8.3 inch11.7 inch

132 Acme Mathematics 7Now, 10 times perimeter = 10 × 2 km = 20 km = 20 kmThus, the distance covered by a man is 20 km.Example 8 How long wire is needed to fence a square field of 30 meters long by 5 times. Solution : Here, length of one side of a square field (l) = 30 m Perimeter of the square field = 4l= 4 × 30 m = 120 m Now, 5 times of perimeter = 5 × 120 m = 600 m Hence, 600 m long wire is needed to fence a square field by 5 times. Example 9 The length of the rectangular field is double its breadth. If the perimeter is 240 m, find the length and breadth of the field. Solution : Let, breadth of the field = x metre then, length of the field = 2x metreGiven that, Perimeter of the field = 240 m Now, Perimeter = 2 (l + b) or, 240 m = 2 (2x + x) or, 240 = 2 × 3x or, 240 = 6x or, 6x = 240 or, x = 40Hence, Length of field = 2 x = 2 × 40 = 80 m and Breadth of field x = 40 mClasswork1. Fill in the blanks. (a) Perimeter of triangle is .......... of all sides. (b) The perimeter of given square is ......... cm. (c) The perimeter of give rectangle is .......... cm. DAxC2x B2 cm2 cm8 cm1 cm

Acme Mathematics 7 1332. Write the perimeter of the given figures:(a)3 cm4 cm2 cmIts perimeter = ................. cm(b)3 cm4 cm 3 cmIts perimeter = ................. cm(c)3 cm3 cm2 cm 2 cmIts perimeter = ................. cm(d)2 cm2 cm2 cm 2 cmIts perimeter = ................. cm(e)` 4 cm2 cm3 cm5 cmIts perimeter = ................. cm(f)3.5 cm4 cm3 cm4 cm6 cmIts perimeter = ................. cm

134 Acme Mathematics 7Exercise 3.11. Fill in the blanks.(a) Perimeter of the quadrilateral is .......................... of its all sides.(b) Perimeter is .................................(c) Perimeter of triangle having each side 'a' cm is .................. cm (d) Perimeter of rectangle having sides 'a' cm and 'b' cm is ..............cm. (e) Perimeter of pentagon is .............................2. Measure the sides of the following triangles and calculate its perimeter [use your scale]:(a) (b)AB = ...........BC = ...........CA = ...........Perimeter = .............................................................................................(c) (d)................................................................................................................................................................................................(e) ................................................................................................(f) ................................................................................................3. Complete the table:Length (l) Breadth (b) l + b 2(l + b)2 cm 1 cm3 cm 2 cmCA BPQ RPO QE FGEFGPQR

Acme Mathematics 7 135Length (l) Breadth (b) l + b 2(l + b)4 cm 2 cm4 cm 3 cm5 cm 3 cm4. Complete the table:Length (l) Breadth (b) 4 l 4 b4 cm 4 cm3 cm 3 cm5 cm 5 cm10 cm 10 cm12 cm 12 cm5. If a , b and c are the sides of triangle and P is it's perimeter. Complete the table:a + b b + c c + a 2 (a + b + c) Perimeter (P)9 cm 11 cm ............... 30 cm 15 cm............ 14 cm 12 cm 40 cm ..................7 cm ............... 8 cm ............... 12 cm14 cm 14 cm ................ 42 cm ................ 6. Calculate the perimeter of the following rectangular objects.(a) (b) (c)(d) (e) (f)7. Find the perimeter of the square whose each sides are: (a) 5 cm (b) 5.5 cm (c) 6 cm (d) 7 cm 21 cm29 cm18 cm12 cm 10 cm18 cm25 cm15 cm 6 cm5 cm 12 cm 8 cm

136 Acme Mathematics 78. Length of the sides of the triangles are given below. Find their perimeter. (a) 3 cm, 4 cm and 5 cm (b) 1.7 cm, 2.8 cm and 4.1 cm(c) 6 cm, 6.5 cm and 8 cm (d) 2.5 cm, 3 cm and 4 cm (e) 10 cm, 2 cm and 9 cm (f) 7 cm, 8 cm and 10 cm 9. Find the perimeter of the rectangle whose lengths and breadths are given below. (a) Length = 10 cm and breadth = 8 cm (b) Length = 15 cm and breadth = 12.5 cm(c) Length = 20.5 cm and breadth = 18.3 cm(d) Length = 25 cm and breadth = 15.9 cm 10. The perimeter and length of a rectangular field are 780 meter and 200 meter respectively. Find the breadth of the field. 11. Find the length of fencing wire of a triangular field with sides 17 m, 15 m and 20 m. 12. A window in the shape of a rectangle surmounted by an isosceles triangle as shown in the adjoining figure. Find the perimeter of the window. 13. The perimeter of a rectangular sheet of paper is 100 cm find its length if its breadth is 19 cm.14. The perimeter of a rectangle and a square are same. If the length and breadth of the rectangle are 14 cm and 12 cm respectively, find the length of the side of the square. 15. Calculate the value of x when, (a) In a triangle, each side are (x – 1) cm and perimeter 18 cm. (b) In a rectangle, length = 4x, breadth = x and perimeter 100 cm. (c) In a square, each sides are (3x – 2) cm and perimeter 100 cm.16. The perimeter of an equilateral triangle is 21 ft., find the length of its each side.17. The perimeter of an isosceles triangle is 40 ft. and the length of each equal side is 12 ft. Find the length of its base.18. The perimeter of a triangle is 90 cm, its two sides are 20 cm and 30 cm, find the measure of third side.Project WorkMeasure the dimension of 'desk', 'table', 'board' and 'class room'. Calculate the perimeter of all and present it to your 'math corner'.5 cm5 cm 3 cm 3 cm4 cm4 cm20 cm30 cm?Perimeter = 90 cm

Acme Mathematics 7 137B Surface area of a cube and a cuboidWarm Up Test1. Write the area of base only in the blanks. (Count the unit cube.)(a) (b)A = .................. cm2 A = .................. cm2(c) (d)A = .................. cm2 A = .................. cm2(e) (f)A = .................. cm2 A = .................. cm22. Write the area of base only in the blanks.(a)1 cm1 cm 1 cm(b)1.5 cm 1.5 cm 1.5 cm(c)2 cm 2 cm2 cmA = .................. cm2 A = .................. cm2 A = .................. cm2(d)5 cm1 cm2 cm(e)2 cm6 cm1 cm(f)4 cm2 cm1 cmA = .................. cm2 A = .................. cm2 A = .................. cm2

138 Acme Mathematics 7(a) Surface area of a cube Consider the net of a cube CubeNet of cubeOne face of a cube21 3 1 6342 5aa a 2Let the length of a side of a cube = a unit. Then area of one face of a cube = a2 square unit. There are 6 faces of equal size in a cube. So that area of cube = a2 + a2 + a2 + a2 + a2 = 6a2Thus, total surface area of a cube (A) = 6a2(b) Surface area of a cuboidConsider the net of a cuboid. Let the length of cuboid = l,Breadth of cuboid = b and Height of cuboid = h Then we have 6 rectangular parts as lC blA B hhb(A + A) + (B + B) + (C + C) = 2A + 2B + 2C Now, Area of A = b × h = bh Area of B = l × h = lh Area of C = l × b = lb Hence, Total surface area (A) = 2bh + 2lh + 2lb or A = 2(bh + lh + lb) Thus, total surface area of a cuboid, A = 2(lb + bh + lh) square unit. bhlCuboidllbBA Chb AhhhBCNet of cuboidb

Acme Mathematics 7 139Solved ExampleExample 1 Find the total surface area of the given cube. Solution: Here, Length of side (a) = 3 cm Now, Total surface area of cube (A) = 6a2= 6 × (3 cm)2= 6 × 9 cm2 = 54 cm2Thus, total surface area of a cube is 54 cm2. Example 2 A rectangular box has length 10 cm, breadth 8 cm and height 6 cm. Find its total surface area. Solution: Here, Length of the cuboid (l) = 10 cmBreadth of the cuboid (b) = 8 cm Height of the cuboid (h) = 6 cm Now, Total surface area of cuboid (A) = 2 (lb + bh + lh) or, A = 2 (10 × 8 + 8 × 6 + 10 × 6) cm2= 2 (80 + 48 + 60) cm2= 2 × 188 cm2 = 376 cm2Hence, the area is 376 cm2.Example 3 Study the given cube and calculate its total surface area if its upper part (lid) is opened. Solution: Here, Length of side (a) = 5 cm In the figure, the upper part is lid-less. So, its has only 5 faces.Now, Total surface area of cube (A) = 5a2= 5 × (5 cm)2= 5 × 25 cm2 = 125 cm2Thus, total surface area of a cube is 125 cm2. Classwork1. Unit cube is used for the following cube and cuboids. Study the cube and cuboids and fill in the blanks:(a) Length of cuboid = ...................................Breadth of cuboid = ....................................Height of cuboid = ....................................Total surface area of cuboid = ....................................3 cm3 cm3 cm8 cm10 cm6 cm5 cm5 cm5 cm

140 Acme Mathematics 7(b) Length of cuboid = ...................................Breadth of cuboid = ....................................Height of cuboid = ....................................Total surface area of cuboid = ....................................(c) Length of cube = ...................................Breadth of cube = ....................................Height of cube = ....................................Total surface area of cube = ....................................2. Find the total surface area of the given solids.(a) (b) (c)(d) (e) (f)(g) (h) (i)Exercise 3.21. Study the net of cuboid and then answer the following questions. (a) Which face is opposite to face 1? (b) Which face is opposite to face 2? (c) Which face is opposite to face 4? 6 cm2 cm 1 cm4 cm 2 cm2 cm3 cm3 cm4 cm1.5 cm 1.5 cm 1.5 cm2 cm 2 cm2 cm4 cm4 cm 4 cm4.5 ft 4.5 ft4.5 ft1 cm1.5 cm8 cm0.5 cm3 cm2.5 cm1 6253 4

Acme Mathematics 7 1412. Calculate the total surface area of the given cuboid whose length, breadth and height are as follows. (a) Length = 10 cm, breadth = 8 cm and height = 5 cm (b) Length = 7 cm, breadth = 5 cm and height = 4 cm (c) Length = 4.3 cm, breadth = 3.2 cm and height = 7.1 cm 3. Calculate the total surface area of the given cube, whose length of each side are:(a) 5 cm (b) 6.3 cm (c) 5.5 cm (d) 10 m 4. A plastic box 1.5 m long, 1.25 m wide and 0.5 m deep is made. It is open at the top. Find the total surface area of the box. 5. Study the given cube and cuboids. Measure its length, breadth and height. Calculate the total surface area if their upper part (lid) is opened.(a) (b) (c)6. A classroom is 7 m long, 6 m wide and 5 m high. (a) Find the area of its floor.(b) Find the area of its 4 walls. 7. A rectangular block is 12 cm long and 8 cm wide. If the total surface area of the block is 392 cm2, find its height. 8. The total surface area of a rectangular box is 992 cm2. If it is 18 cm long and 8 cm high, find its breadth. 9. The breadth and height of a cuboids are 10 cm and 5 cm respectively. If its total surface area is 550 cm2, find its length. 10. Calculate the length of edge of the following cubes whose total surface area is given. (a) 96 cm2 (b) 216 cm2 (c) 600 cm2 (d) 150 cm2

142 Acme Mathematics 7C Volume of cuboid and cubeWarm Up Test1. Count the number of the cubes and write the volume of each block [Note : volume of each cube is 1 cm3](a) (b) (c)6 cm3 Volume = cm3 Volume = cm3 Volume =(d) (e) cm3 Volume = cm3 Volume =(f) (g) cm3 Volume = cm3 Volume =2. Fill in the blanks : (Count the unit cube.)(a) (b)V = .................. cm3 V = .................. cm3

Acme Mathematics 7 143(c) (d)V = .................. cm3 V = .................. cm3(e) (f)V = .................. cm3 V = .................. cm33. Unit cube is used for the following cuboids. Study the cuboids and fill in the blanks:(a) Length of cuboid = ...................................Breadth of cuboid = ....................................Height of cuboid = ....................................Volume of cuboid = ....................................(b) Length of cuboid = ...................................Breadth of cuboid = ....................................Height of cuboid = ....................................Volume of cuboid = ....................................(c) Length of cuboid = ...................................Breadth of cuboid = ....................................Height of cuboid = ....................................Volume of cuboid = ....................................

144 Acme Mathematics 7(a) Volume of a cuboid Consider the given figure. It is a cuboid. Its length = lbreadth = b and height = h Now, volume of a cuboid is calculated by the product of length, breadth and height. Thus, Volume (V) = length × breadth × height. V = l × b × h cubic unit Now, Remember(i) V = l × b × h (ii) l = Vb × h, to calculate length(iii) b = Vl × h, to calculate breadth (iv) h = Vl × b , to calculate height(b) Volume of a cube The adjoining figure is cube. Its length, breadth and height are equal. Let, length of each side = a unit Then, its volume = length × breadth × height V = a × a × aV = a3Thus, volume of cube = a3V = a3 cubic unit Now, RememberLength of each side of a cube (a) = V3RememberVolume of liquid are measured in litres and millilitre.Where, 1 litre = 1000 ml = 1000 cm3So, 1 ml = 1 cm3or, 10 cm × 10 cm × 10 cm = 1000 cm3 = 1 litre.10 cm10 cm10 cmv = 1000 cm31 litreV = l × b × h BreadthHeightLengthaaaV = a3

Acme Mathematics 7 145Solved ExampleExample 1 Calculate the volume of the given chalk box. Solution: Here, Length of chalk box (l) = 6 cm Breadth of chalk box (b) = 5 cm Height of chalk box (h) = 4 cm It is cuboid. So, volume = l × b × h = 6 cm × 5 cm × 4 cm = 120 cm3The volume of the chalk box is 120 cm3. Example 2 If the volume of the die is 64 cm3, find the length of its side. Solution: Die is a cube. Volume of cube (V) = 64 cm3let, Length of cube (l) = x cm Now, Length of cube = V3 cmx = 64 3or, x = 4 The length of its side is 4 cm.Classwork1. Match the following, where l, b, h and V have their usual meaning.volume of Cube 5 faces onlylength of cuboid l × b × hlength of cube l3volume of cuboid Vb × hlid less cube l 32. Write the volume of the given cube in the blanks.(a)2 cm2 cm2 cm(b)3 cm 3 cm3 cm(c)2.5 cm 2.5 cm 2.5 cmV = ............... cm3 V = ............... cm3 V = ............... cm36 cm5 cm 4 cm

146 Acme Mathematics 73. Write the volume of the given cuboids in the blanks.(a)10 cm6 cm4 cm(b)4 cm12 cm2 cm(c)8 cm4 cm2 cmV = ............... cm3 V = ............... cm3 V = ............... cm3Exercise 3.31. Find the volume of cuboids with the following measure. (a) Length = 10 cm, breadth = 8 cm and height = 2 cm (b) Length = 5 cm, breadth = 4.5 cm and height = 2.5 cm (c) Length = 15.5 cm, breadth = 10.5 cm and height = 7.0 cm 2. Find the volume of cubes with the following measure. (a) Length = 5 cm (b) Length = 6.5 cm (c) Length = 4.3 cm 3. Our water tank is 9 m long and 2 m high. If its volume is 108 m3. Find its breadth. 4. A match box is 3 cm broad and 1 cm high. If the volume of the match box is 12 cm3, find the length of match box.5. A wooden block's volume is 124.75 cm3. If its length and breadth are 10 cm and 5.5 cm, find its height.6. A cubical tank has volume 1728 cm3. Find the length of side of the tank. 7. A cuboid has volume 1000 cm3. If length is double of its breadth and height is 5 cm, calculate the length and breadth of the cuboid.8. Find the volume of this solid:9. The aquarium is 2 meter long, 1.5 meter broad and 50 cm high. How many litres of water does it hold? If we want to empty it, how many times does a cube 10 cm × 10 cm × 10 cm can empty it?8 cm 10 cm12 cm5 cm 4 cm

Acme Mathematics 7 14710. An oil storage tank is being designed to hold 1250 litre of oil. It has to be fitted into a space 1.8 meter long and 1.5 meter breadth. What height should the tank be?11. A manufacturer has to decide which of these shapes of box to use for his chocolates?(a) Which box has the greater volume.(b) Which box uses more card-board.(c) Which box do you think the manufacturer should choose.12. Copy and complete this table for cubes. Length of edge (cm) 1 2 4 5 6 ... ... ... NPerimeter of edges (cm)Total surface area of faces (cm2)Volume (cm3)13. Calculate the length of the edges of cubes which have :(a) Perimeter of 600 cm.(b) Total surface area (TSA) of 2400 cm2(c) Volume of 1000 cm314. Can you find the volume and surface area with out a picture? Complete the table.Cube Volume (cm3) Total Surface Area (cm2)1 1 62 8 243 -4 -5 -6 -7 -20 cm 10 cm20 cm40 cm5 cm20 cmBox - 'A'Box - 'B'1 cm1 cm 1 cm

148 Acme Mathematics 7Project Work1. Objective : To find the total surface area and volume.2. Materials required :measuring tape, pen and paper3. Activities:” Measure the length, breadth and height of the given objects and complete the table.Classroom Math book Chalk box Your bed roomLength breadth heightNow, solve the following questions.(a) Calculate the total surface area.(b) Calculate the volume.

Acme Mathematics 7 149Project Work1. Objective: To construct a cuboid2. Materials required :” card board” pair of scissors, ” pencil, ” scale, ” colours, ” gum, etc.3. Activity:” Here is a net of cuboid. Use it to make cuboid.I know how to construct cuboid.

150 Acme Mathematics 73.2 CircleLook at the given figure:All objects are circular in shape. A circle is a closed figure. Circle is not bounded by straight lines. It is bounded by curved line. Points A, B and C are on the curved line. O is the point equidistant from the points A, B and C. O is called the 'centre' of the circle. OA is called the 'radius' of the circle. XY is the line segment through centre of the circle O. It is called the 'diameter'. The diameter of a circle is twice the radius. (a) Chord of a circleXY and AB are the chords of the circle. We can draw large number of chords. Diameter is the longest chord. (b) Arc and semicircleThe part of the circle is called the arc of the circle. AB is the arc of the given circle. Half of a circle is called a semicircle. ABC is a semicircle. The perimeter of the circle is called the circumference. C AOBX YOABOA BOADBCO