142 Mathematics Grade 5 Danny is drawing a floor plan of his classroom to a scale of 1 : 250. The length of his classroom in his floor plan is 5 cm. What is the actual length of his classroom in metres? 1 : 250 = 5 : 5 ÷ 1 = × cm = cm The actual length of Danny’s classroom is cm. 100 cm = 1 m cm = ÷ 100 = m The actual length of Danny’s classroom is m. A tower is drawn to a scale of 1 : 1500 in a brochure. The height of the tower in the brochure is 7 cm. Find the actual height of the tower in metres. 1 : 1500 = 7 : ÷ = × cm = cm The actual height of the tower is cm. 100 cm = 1 m cm = ÷ = m The actual height of the tower is m.
143 CHAPTER 6 Ratio A 200-m long street is drawn to a scale of 1 : 5000 on a map. What is the length of the street on the map? Give your answer in cm. 1 m = 100 cm m = × = cm The actual length of the street is cm. 1 : 5000 = : ÷ 5000 = × = The length of the street on the map is cm. Practice 1. Using a ruler, measure the length of the figure. Then, answer the questions. Scale 1 : 15 (a) What is the height of the diagram of the table lamp above? (b) What is the actual height of the table lamp? First, express 200 m in cm.
144 Mathematics Grade 5 2. A road is drawn using a scale of 1 : 1200 in a diagram. If the road is 10 cm long in the diagram, what is the length of the actual road? Give your answer in metres. 3. On a map, the distance between the town library and the school is 6 cm. The actual distance between them is 2.4 km. (a) What is the scale of the map? (b) Lily discover that the distance between her house and the school is 8 cm. What is the actual distance between Lily’s house and the school? Give your answer in km.
Chapter 7 Speed Learning Outcomes You should be able to • find speed, time and distance using formula • find average speed • understand and write in different units such as km/h, m/min, m/s and cm/s • solve word problems involving speed Does the rabbit or the tortoise run faster? How can we measure their speed? https://qr.pelangibooks.com/?u=MOMG5C7mo1 https://qr.pelangibooks.com/?u=MOMG5C7mo2 https://qr.pelangibooks.com/?u=MOMG5C7mo3 4 https://qr.pelangibooks.com/?u=MOMG5C7mo4 Maths Online I can complete the race in 500 seconds. I can complete the race in 10 seconds. Maths Online Maths Online Maths Online Maths Online 2 3 4
Mathematics 146 Grade 5 A Distance and speed John and Nadia take parts in a cross country. In an hour, John runs 3 km. Nadia runs 2.8 km. John runs at a speed of 3 km per hour. Nadia runs at a speed of 2.8 km per hour. We can write the running speed of John as 3 km/h. The running speed of Nadia is 2.8 km/h. A car travels 80 km in an hour. What is its speed? Its speed is 80 km/h. Marina cycles 6 km in an hour. What is her speed? Her speed is km/h. A pingpong ball rolls 10 cm in a second. What is its speed? Its speed is cm/s. The speed tells how fast somebody moves. Speed is expressed as distance travelled per unit time. The symbol “/” is read “per”. We read 3 km/h as 3 km per hour. Nadia John watch me
CHAPTER 7 Speed 147 A motorcycle travels at a speed of 65 km/h. In an hour, the motocycle travels km. Basri runs at a speed of 11 m/s. In a second, Basri runs m. Mr Lee drives his car at a speed of 70 km/h. How far can he travel in (a) 2 hours? (b) 5 hours? (a) 1 h 70 km 2 h 2 × 70 km = 140 km Mr Lee can travel 140 km in 2 hours. (b) 5 h 5 × 70 km = 350 km Mr Lee can travel 350 km in 5 hours. A cyclist is cycling at a speed of 15 km/h. What distance can he travel in 3 hours? 1 h km 3 h × km = km He can travel km in 3 hours. Distance = Speed × Time Recall: 15 km/h is read as 15 km per hour. MATHS TIPS D = S × T ( Distance = Speed × Time ) S = D ÷ T ( Speed = Distance ÷ Time ) T = D ÷ S ( Time = Distance ÷ Speed ) D S T
148 Mathematics Grade 5 A snail moves at a speed of 2 cm/s. How far can it travel in 30 seconds? 1 s 2 cm 30 s 30 × 2 cm or Speed = 2 cm/s Time = 30 s Distance = Speed × Time = 2 × 30 = cm = cm It can travel cm in 30 seconds. A bus travels at a speed of 65 km/h. How far can it travel in 4 hours? 1 h km 4 h × km or Speed = km/h Time = h Distance = × = km = km It can travel km in 4 hours. Rahmat’s walking speed is 120 m/min. How far can he walk in 5 minutes? 1 min m 5 min × m or Speed = m/min Time = min Distance = × = m = m He can walk m in 5 minutes.
CHAPTER 7 Speed 149 A lorry travels 225 km in 3 hours. What is the lorry’s speed in km/h? 3 h 225 km 1 h 225 km ÷ 3 = 75 km The lorry’s speed is 75 km/h. or Distance = 225 km Time = 3 h Speed = Distance ÷ Time = 225 ÷ 3 = 75 km/h The lorry’s speed is 75 km/h. A train travelled a distance of 208 km in 2 hours. Find its speed. 2 h km 1 h km ÷ or Distance = km Time = h Speed = Distance ÷ Time = ÷ = km/h = km It speed is km/h. Speed = Distance ÷ Time The lorry’s speed in km/h means the distance (in km) covered by the lorry in an hour.
150 Mathematics Grade 5 Sally walks to school every day at a speed of 120 m/min. The distance between Sally’s house and her school is 840 m. How long does Sally take to walk from her house to her school? 120 m 1 min 840 m 840 120 = 7 min Sally takes 7 minutes to walk from her house to school. or Distance = 840 m Speed = 120 m/min Time = Distance ÷ Speed = 840 ÷ 120 = 7 min Sally takes 7 minutes to walk from her house to school. The distance between Town A and Town B is 195 km. Adam rides his motocycle at a speed of 65 km/h from Town A to Town B. How long does Adam take to travel? km 1 h km or Distance = km Speed = h Time = Distance ÷ Speed = ÷ = h = h Adam takes h to travel. 7 1 Time = Distance ÷ Speed
CHAPTER 7 Speed 151 Practice 1. A bus took 2 hours to travel 180 km. What is the speed of the bus? 2. A toy car moved 750 m at a speed of 250 m/min. How long did it take to cover the distance? 3. John jogged at a speed of 95 m/min for 45 minutes. How far did he jog?
Mathematics 152 Grade 5 B Average speed Notice that the speed of the car from Town X to Town Y and that of Town Y to Town Z is different. Let’s look at the figure below. Town X Town Y Town Z 130 km 320 km Mr Adi drove for 2 h from Town X to Town Y. Then, he drove another 3 h to Town Z. What was Mr Adi’s average driving speed from Town X to Town Z? Average speed measures how far an object moved over a given period of time. Average speed = Total distance travelled Total time taken Total distance travelled = 130 km + 320 km = 450 km Total time taken = 2 h + 3 h = 5 h Average speed = 450 5 = 90 km/h Mr Adi’s average driving speed from Town X to Town Z is 90 km/h. 90 Total distance = Distance from Town X to Town Y + Distance from Town Y to Town Z 1 watch me
CHAPTER 7 Speed 153 Amy took part in a 200 m running race. She ran the first 100 m in 12 seconds and covered the rest of the distance in 13 seconds. Find Amy’s average speed. Total distance run = m Total time taken = s + s = s Average speed = Total distance travelled Total time taken = = m/s Amy’s average speed is m/s. A bus travelled at a speed of 80 km/h for 2 hours. It then increased its speed and travelled at a speed of 90 km/h for the next 3 hours. (a) What was the total distance travelled by the bus? (b) What was its average speed? (a) First part of journey = 80 × 2 = 160 km Second part of journey = 90 × 3 = 270 km Total distance = 160 + 270 = 430 km The total distance travelled by the bus is 430 km. (b) Average speed = 430 5 = 86 km/h Its average speed is 86 km/h. Distance = Speed × Time
154 Mathematics Grade 5 In a walkathon, Nina walked at a speed of 150 m/min for 30 min. She then slowed down and walked at a speed of 120 m/min for 70 min. (a) Find the total distance Nina had walked. (b) Find Nina’s average speed. (a) First part of the journey = × = m Second part of the journey = × = m Total distance = m + m = m The total distance Nina had walked was m. (b) Total time taken = min + min = min Average speed = = m/min Nina’s average speed was m/min. Average speed = Total distance travelled Total time taken
CHAPTER 7 Speed 155 Mrs Sumanto was driving from City A to City B. She covered the first part of her journey in 1 1 2 h. She drove another 250 km at an average speed of 100 km/h. The distance between City A and City B is 430 km. (a) Find the total time taken for Mrs Sumanto to drive from City A to City B. (b) Find her average speed for the whole journey. (a) Time taken for first part of the journey = 1 1 2 h Time taken for second part of the journey = 250 100 = 5 2 = 2 1 2 h Total time taken = 1 1 2 h + 2 1 2 h = 4 h The total time taken for Mrs Sumanto to drive from City A to City B was 4 h. (b) Average speed = Total distance travelled Total time taken = 430 4 = 215 2 = 107.5 km/h Her average speed for the whole journey is 107.5 km/h. 215 2 2 5
156 Mathematics Grade 5 Ramil walked 6 minutes from his house to the bakery. He then walked another 810 m at a speed of 90 m/min from the bakery to school. Ramil walked 1500 m in total. (a) Find the total time taken to cover the whole distance. (b) Find Ramil’s average speed for the whole distance. (a) Time taken to walk from Ramil’s house to the bakery = 6 min Time taken to walk from the bakery to school = = min Total time taken = min + min = min The total time taken to cover the whole distance is min. (b) Average speed = Total distance travelled Total time taken = = m/min. Ramil’s average speed for the whole distance is m/min. Time = Distance ÷ Speed
CHAPTER 7 Speed 157 Practice 1. Andy jogged at a speed of 100 m/min for 40 min. He then increased his speed and jogged at 125 m/min for another 40 min. (a) What was the total distance Andy jogged? (b) What was Andy’s average speed? 2. A bus travelled 1 1 2 h for the first part of its journey. Then, the bus travelled the remaining 360 km at a speed of 120 km/h. The bus travelled 465 km in total. (a) Find the total time taken for the whole journey. (b) Find the average speed of the bus for the whole journey.
Mathematics 158 Grade 5 C Word problems Idris took 30 min to cycle from his house to the library at the speed of 120 m/min. On his return journey, he cycled 150 m/min. How long did Idris take to reach home? Idris’s house Library 120 m/min, 30 min 150 m/min, ? min Distance between Idris’s house and the library = Speed × Time = 120 × 30 = 3600 m Time taken to cycle home from the library = Distance ÷ Speed = 3600 ÷ 150 = 24 min Idris took 24 min to reach home. First, find the distance between Idris’s house and the library. Distance = Speed × Time watch me
CHAPTER 7 Speed 159 Priya threw a paper plane to Natalia. It flew at a speed of 40 cm/s and reach Natalia in 3 seconds. Natalia then threw the paper plane back at Priya, and it reached her in 6 seconds. What was the speed of the paper plane when it flew from Natalia to Priya? Priya Natalia 40 cm/s, 3s ? cm/s, 6s Distance between Priya and Natalia = × = cm Speed of the paper plane flying from Natalia to Priya = Distance ÷ Time = ÷ = cm/s The speed of the paper plane when it flew from Natalia to Priya was cm/s. Farid ran a total distance of 10 km. He ran the first 4 km at 250 m/min and then jogged the remaining 6 km in 34 minutes. What was his average speed for the whole journey in m/min? 4 km, 250 m/min 6 km, 34 min Time taken for the first 4 km = 4000 250 = 16 min Total time taken = 16 min + 34 min = 50 min Average speed = = m/min His average speed for the whole journey was m/min. 1 km = 1000 m 4 km = 4000 m 10 km = ? m 16 1
160 Mathematics Grade 5 Ms Nora drove from Town A to Town B. She covered 1 3 of the journey in the first 2 hours. She then drove the remaining 210 km in 3 hours. (a) Find Ms Nora’s average speed for the whole journey. (b) Find the distance between Town A and Town B. Town A Town B 2 h 3 h ? km 210 km ? km (a) 2 units 210 km 1 unit 210 2 = 105 km 3 units 3 × 105 km = 315 km The distance between Town A and Town B is 315 km. (b) Total time taken = 2 h + 3 h = 5 h Average speed = Total distance travelled Total time taken = 315 5 = 63 km/h Ms Nora’s average speed for the whole journey is 63 km/h. 105 1
CHAPTER 7 Speed 161 Hadi cycled from his house to the park. He took 12 minutes to travel 4 5 of the journey and 3 minutes to travel the remaining 1500 m. (a) Find the distance between Hadi’s house and the park. (b) Find the average speed for the whole journey. Hadi’s House Park min min ? m m ? m (a) 1 unit m 5 units × = m The distance between Hadi’s house and the park is m. (b) Total time taken = min + min = min Average speed = Total distance travelled Total time taken = = m/min The average speed for the whole journey is m/min.
162 Mathematics Grade 5 A car and a motocycle are travelling from Village X to Village Y. The car moves at a speed of 80 km/h and the motocycle moves at a speed of 60 km/h. Both vehicles leaves Village X at the same time. (a) After 2 hours, what is the distance between the car and the motorcycle? (b) Given that the distance between Village X and Village Y is 240 km, how long does the motorcycle take to reach Village Y? (a) Distance travelled by car = Speed × Time = 80 × 2 = 160 km The distance travelled by motorcycle = 60 × 2 = 120 km Distance between the car and the motorcycle = 160 km – 120 km = 40 km After 2 hours, the distance between the car and the motorcycle is 40 km. (b) Time = Distance Speed = 240 60 = 4 h The motorcycle takes 4 h to reach Village Y. 4 1
CHAPTER 7 Speed 163 A van and a lorry travel from Town A to Town B at 90 km/h and 75 km/h respectively. They both leave Town A at the same time. If the van reaches Town B after 5 hours, (a) What is the distance between Town A and Town B? (b) How long does the lorry take to reach Town B? (a) Distance travelled by the van = Speed × Time = × = km The distance between Town A and Town B is km. (b) Time taken for lorry to reach Town B = Distance Speed = = h The lorry takes h to reach Town B.
164 Mathematics Grade 5 Practice Solve the following word problems. 1. Arief took 5 minutes to walk from his house to the park at a speed of 96 m/min. He then took 6 minutes to walk from the park back to his house. (a) What was the distance between Arief’s house and the park? (b) What was his speed for the return trip? 2. Putri drives from City A to City B. She covers 3 4 of her journey in 2 1 5 h. She covers the remaining 80 km in 2 5 h. (a) Find the total time taken for her whole journey. (b) Find Putri’s average driving speed for the whole journey.
Chapter 8 Volume of cubes and cuboids You should be able to • calculate the volume of cubes and cuboids • solve word problems related to volume and capacity of cuboids Learning Outcomes How can we find out which of the two solids has a greater volume? https://qr.pelangibooks.com/?u=MOMG5C8mo1 https://qr.pelangibooks.com/?u=MOMG5C8mo2 https://qr.pelangibooks.com/?u=MOMG5C8mo3 4 https://qr.pelangibooks.com/?u=MOMG5C8mo4 Maths Online Maths Online Maths Online Maths Online Maths Online 2 3 4
166 Mathematics Grade 5 A Drawing cubes and cuboids Let’s look at the figure below. It is a unit cube drawn on a dot paper. Unit cube We can draw cubes of different lengths on a dot paper. 2 units 2 units 2 units Let’s Think! Look at the unit cubes below. What do you notice? When two unit cubes are drawn in this way, we get a cuboid. watch me
CHAPTER 8 Volume of cubes and cuboids 167 We can also draw cuboids of different sizes in different orientations on dot paper. Do you know how are these cuboids drawn? 2 units 1 unit 1 unit 3 units 1 unit 1 unit The figure below shows cubes and cuboids drawn on a dot paper. Can you differentiate them?
168 Mathematics Grade 5 Complete the following drawings of cubes or cuboids. 1. 2. 3. 4. 5. 6. Practice
CHAPTER 8 Volume of cubes and cuboids 169 The volume of a solid is the amount of space occupied by the solid. 1 unit 1 unit 1 unit Face Edge A unit cube is a cube that has 1-unit long edges. The unit cube occupies a space of 1 cubic unit. The volume of the unit cube is 1 cubic unit. This solid is made up of 6 unit cubes. Its volume is 6 cubic units. This solid is made up of 10 unit cubes. Its volume is cubic units. This solid is made up of unit cubes. Its volume is cubic units. B Measuring volume watch me
170 Mathematics Grade 5 This cube has edges with the length of 1 cm. This cube occupies a space of 1 cubic centimetre (cm3 ). The volume of the unit cube is 1 cm3 . This solid is made up of four 1-cm cubes. Its volume is cm3 . This solid is made up of 1-cm cubes. Its volume is cm3 . 1 m 1 m 1 m This cube has edges with the length of 1 m each. This cube occupies a space of 1 cubic metre (m3 ). The volume of the unit cube is 1 m3 . This solid is made up of 1 - m cubes. Its volume is m3 . This solid is made up of 1- m cubes. Its volume is m3. 1 cm 1 cm 1 cm
CHAPTER 8 Volume of cubes and cuboids 171 Let’s look at the cuboid below. It is made up of sixteen 1-cm cubes. Height Breadth Length Length of cuboid = 3 cm Breadth of cuboid = 2 cm Height of cuboid = 2 cm Volume of cuboid = 16 cm3 The cuboid below is made up of 1-cm cubes. Height Breadth Length Length of cuboid = cm Breadth of cuboid = cm Height of cuboid = cm Volume of cuboid = cm3 The cuboid below is made up of 1-m cubes. Height Breadth Length Length of cuboid = m Breadth of cuboid = m Height of cuboid = m Volume of cuboid = m3 The cuboid below is made up of 1-m cubes. Height Breadth Length Length of cuboid = m Breadth of cuboid = m Height of cuboid = m Volume of cuboid = m3
172 Mathematics Grade 5 Practice 1. Assuming that 1 indicates 1 cubic unit, find the volume of the solids in cubic units, by counting the cubes. (a) (b) 2. Assuming that 1 indicates 1 cm3 , find the volume of the solids in cm3 , by counting the cubes. (a) (b) 3. Fill in the correct answers. (a) 25 cm 10 cm 10 cm (b) 12 cm 12 cm 12 cm Length = Length = Breadth = Breadth = Height = Height = This solid is a This solid is a
CHAPTER 8 Volume of cubes and cuboids 173 C Finding cubes and cube roots When the number is multiplied by itself three times, we say that the number is cubed. 2 × 2 × 2 = 8 In this case, we say that the cube of 2 is 8. We write 23 = 8. We read 23 as “cube of 2”. What is the cube of 3? The cube of 3 is × × . We write it as . What is the cube of 5? The cube of 5 is × × . We write it as . Practice Complete the following drawings of cubes or cuboids. 1. Find the value of 33 . 2. Find the value of 63 . 33 = × × 63 = × × = = 3. What is the value of 103 ? 4. What is the value of 123 ? 103 = × × 123 = × × = = Recall: We read 22 as "square of 2". 22 = watch me
174 Mathematics Grade 5 What is a cube root? A cube root goes the opposite direction of cube. 8 = 2 × 2 × 2 The cube root of 8 is 2. We write 3 8 = 2. We read 3 8 as "the cube root of 8". What is the cube root of 27? What is the cube root of 64? 27 = × × . 64 = × × . 3 27 = 3 64 = What is 3 125 ? Find the value of 3 343 . 343 = 7 × 49 = 7 × × Therefore 3 343 = . 125 = 5 × 25 = 5 × 5 × 5 Therefore, 3 125 = 5. What is 3 512 ? What is 3 729 ? 729 = 3 × 243 = 3 × 3 × 81 = 3 × 3 × × Therefore, 3 729 = . 512 = 2 × 256 = 2 × 2 × 128 = 2 × 2 × 2 × 64 = 2 × 2 × 2 × 8 × 8 Therefore, 3 512 = . Write 125 as a product of its prime factors.
CHAPTER 8 Volume of cubes and cuboids 175 Let's learn the cubes and cube roots from 1 to 15. Cube Cube roots 1 × 1 × 1 = 13 = 1 3 1 = 1 2 × 2 × 2 = 23 = 8 3 8 = 2 3 × 3 × 3 = 33 = 27 3 27 = 3 4 × 4 × 4 = 43 = 64 3 64 = 3 5 × 5 × 5 = 53 = 125 3 125 = 5 6 × 6 × 6 = 63 = 216 3 216 = 6 7 × 7 × 7 = 73 = 343 3 343 = 7 8 × 8 × 8 = 83 = 512 3 512 = 8 9 × 9 × 9 = 93 = 729 3 729 = 9 10 × 10 × 10 = 103 = 1000 3 1000 = 10 11 × 11 × 11 = 113 = 1331 3 1331 = 11 12 × 12 × 12 = 123 = 1728 3 1728 = 12 13 × 13 × 13 = 133 = 2197 3 2197 = 13 14 × 14 × 14 = 143 = 2744 3 2274 = 14 15 × 15 × 15 = 153 = 3375 3 3375 = 15
176 Mathematics Grade 5 D Volume of a cuboid and of liquid Volume of a cuboid Look at the cuboid below. 1 cm 1 cm 1 cm What is the volume of this cuboid? The cuboid has twelve 1-cm cubes. Its volume is 12 cm3 . 1 cm 1 cm 1 cm 3 cm 2 cm 2 cm The length of the cuboid is 3 cm. The breadth of the cuboid is 2 cm. The height of the cuboid is 2 cm. The volume of the cuboid = 3 cm × 2 cm × 2 cm = 12 cm3 Besides counting the number of unit cubes, we can find the volume of a cuboid by multiplying its length by its breadth and its height. Volume of cuboid = Length × Breadth × Height watch me
CHAPTER 8 Volume of cubes and cuboids 177 Calculate the volume of the cuboid. Length = 5 cm Breadth = 7 cm Height = 3 cm Volume of cuboid = Length × Breadth × Height = 5 cm × 7 cm × 3 cm = 105 cm³ The volume of the cuboid is 105 cm3 . Find the volume of the cuboid. Length = cm 3 cm 2 cm 4 cm Breadth = cm Height = cm Volume of cuboid = cm × cm × cm = cm³ The volume of the cuboid is cm3 . What is the volume of the following cuboid? Volume of cuboid 15 cm 10 cm 12 cm = cm × cm × cm = cm³ The volume of the cuboid is cm3 . 5 cm 7 cm 3 cm
178 Mathematics Grade 5 Notice that the length, breadth and height of a cube are equal. Volume of a cube Look at the cube below. It's edges are 5 cm long. What is its volume? 5 cm 5 cm 5 cm Length = 5 cm Breadth = 5 cm Height = 5 cm Volume of cube = Length × Breadth × Height = 5 cm × 5 cm × 5 cm = 125 cm³ The volume of the cube is 125 cm3 . What is the volume of the cube? Volume of cube 8 cm 8 cm 8 cm = cm × cm × cm = ³ = cm³ The volume of the cube is cm3 . Find the volume of a cube of edge 12 cm. Volume of cube = cm × cm × cm = ³ = cm³ The volume of the cube is cm3 . The volume of a cube is also equal to Edge × Edge × Edge. 5 × 5 × 5 = 53 = 125
CHAPTER 8 Volume of cubes and cuboids 179 The figure below shows a tank in the shape of a cube. When 1 l of water is poured into it, the tank is completely filled. 1 millilitre (ml) = 1 cubic centimetre (cm3 ) 1 litre (l) = 1000 cubic centimetres (cm3 ) 1 litre (l) = 1000 millilitres (ml) 1 cubic metre (m3 ) = 1000 litres (l) 1 cubic metre (m3 ) = 1 000 000 cubic centimetres (cm3 ) Practice 1. Write the following in cubic centimetres. (a) 400 ml = (b) 3 l = (c) 21 560 ml = (d) 11 l 70 ml = 2. Write the following in litres and millilitres. (a) 669 cm3 = (b) 1500 cm3 = (c) 24 000 cm3 = (d) 50 800 cm3 = Volume of a liquid Volume of water in tank = 10 cm × 10 cm × 10 cm = 1000 cm³ Volume of water 1000 ml = Volume of tank 1000 ml = 1000 cm³ 1 ml = 1 cm³ 10 cm 10 cm 10 cm
180 Mathematics Grade 5 Solving word problems A tank measuring 12 cm by 20 cm by 18 cm is completely filled with water. What is the volume of water in the tank? Give your answer in litres and millilitres. Volume of water in tank = 12 cm × 20 cm × 18 cm = 4320 cm³ = 4320 ml 12 cm 20 cm 18 cm = 4 l 320 ml The volume of water in the tank is 4 l 320 ml. A rectangular container measures 25 cm by 15 cm by 20 cm. What is the capacity of the container? Give your answer in litres and millilitres. Capacity of container = 25 cm × 15 cm × 20 cm = cm³ 25 cm 15 cm 20 cm = ml = l ml The capacity of the container is l ml. Find the volume of water in the rectangular tank below. Give your answer in millilitres. Volume of water = cm × cm × cm = cm³ = ml The volume of water in the tank is ml. 40 cm 15 cm 10 cm
CHAPTER 8 Volume of cubes and cuboids 181 The figure below shows a cubical container. The edge of the container is 12 cm. How many litres and millitres of liquid can this container hold? Capacity of container = cm × cm × cm = cm³ 12 cm = ml = l ml This container can hold l ml of liquid. A tank measuring 15 cm by 12 cm by 10 cm contains 800 ml of water. How much more water is needed to fill the tank completely? Give your answer in milliliters. Capacity of tank = 15 cm × 12 cm × 10 cm = cm³ 15 cm 12 cm 10 cm = ml Volume of water in tank = ml Amount of water needed to fill the tank = ml – ml = ml ml of water is needed to fill the tank completely.
182 Mathematics Grade 5 Practice Solve the following word problems. 1. What is the volume of a cube of edge 12 cm? 2. A cuboid has a length of 6 m and a height of 10 m. It's breadth is 1 2 of its length. What is the volume of the cuboid? 3. The base of a container is a square of edge 14 cm. The height of the container is 16 cm. It is half-filled with water. What is the volume of water in the container? Give your answer in litres and millilitres.
CHAPTER 8 Volume of cubes and cuboids 183 More volume of solids E Let's look at the cuboid below. The breadth of the cuboid is 4 cm. Its height is 3 cm. Given that the volume of the cuboid is 96 cm3 , can you find its length? Volume of cuboid = Length × Breadth × Height Length × 4 cm × 3 cm = 96 cm3 Length × 12 cm2 = 96 cm3 Length = 96 cm3 ÷ 12 cm2 ? 4 cm 3 cm = 8 cm The length of the cuboid is 8 cm. or Length × 4 cm × 3 cm = 96 cm3 Length = 96 4 × 3 24 8 1 1 = 8 cm The length of the cuboid is 8 cm. 96 4 × 3 Therefore, 96 4 × 3 = 96 ÷ 12. This means "divide". watch me
184 Mathematics Grade 5 The volume of a cuboid is 300 cm3 . The length of the cuboid is 6 cm and the breadth is 5 cm. What is the height of the cuboid? 6 cm × 5 cm × Height = 300 cm3 cm × Height = cm3 ? 5 cm 6 cm Height = ÷ = cm or 6 cm × 5 cm × Height = 300 cm3 Height = × = cm The height of the cuboid is cm. The capacity of a rectangular container is 6400 ml. Given that the base area of the container is 800 cm3 , what is the height of the container? Capacity of container = 6400 ml = 6400 cm3 Capacity of container = Length × Breadth × Height = Base area × Height Therefore, Height = Capacity ÷ Base area = 6400 cm3 ÷ 800 cm2 = 8 cm The height of the container is 8 cm. 3 Area = 800 cm ?
CHAPTER 8 Volume of cubes and cuboids 185 The volume of the cuboid shown is 32 cm3 . ? 4 cm2 The area of the square face is 4 cm2 . Find the length of the cuboid. Length × Breadth × Height = 32 cm3 Length × Area of shaded face = 32 cm3 Length = cm3 ÷ cm2 = cm The length of the cuboid is cm. The volume of the cuboid shown is 200 cm3 . It has a length of 8 cm and a square face. What is the length of one side of the square face? ? 8 cm Area of square face × Length = Volume of cuboid Area of square face × 8 cm = 200 cm3 Area of square face = 200 8 25 1 = 25 cm2 ? Area = 25 cm2 Therefore, length of one side = 25 = 5 cm The length of one side of the square face is 5 cm. We can find the length of one side of a square by finding its square root. Side × Side = 25 Side = 25 Volume of cuboid = Length × Area of shaded face = Length × Breadth × Height
186 Mathematics Grade 5 A rectangular tank of volume 490 cm3 has a height of 10 cm and a square face. Find the length of one side of the square face. Area of square face × cm = cm3 10 cm Area of square face = = Length of one side = = cm The length of one side of the square face is cm. The volume of the cuboid shown is 27 cm3 . ? What is the length of one edge of the cube? Volume of the cube = Edge × Edge × Edge 27 cm3 = ? Therefore, Edge = 3 27 = 3 cm The length of one edge of the cube is 3 cm. The cube shown has a volume of 125 cm3 . Find the length of each edge of the cube. Volume of the cube = 125 cm3 Length of one edge = 3 ? = cm The length of one edge of the cube is cm. We can find the edge of a cube by finding its cube root. Edge × Edge × Edge = 27 Edge = 327
CHAPTER 8 Volume of cubes and cuboids 187 Practice Solve the following word problems. 1. Andre has a Rubik's cube. The volume of his Rubik's cube is 216 cm³. What is the length of its edge? 2. What is the length of each edge of a wooden cube that has a volume of 2197 cm³? 3. A rectangular block has a square base. Its length is 20 cm and its volume is 5120 cm³. Find the length of one edge of the square base. 20 cm ?
188 Mathematics Grade 5 More volume of liquids F A tank measuring 20 cm by 5 cm by 10 cm contains 500 ml of water. How much more water is needed to fill the tank completely? Give your answer in milliliters. Capacity of tank = 20 cm × 5 cm × 10 cm 20 cm 5 cm = 1000 cm³ 10 cm = 1000 ml Volume of water in tank = 500 ml Amount of water needed = 1000 ml – 500 ml = 500 ml 500 ml more water is needed to fill the tank completely. A container has a height of 12 cm and a square base of side 9 cm. The container is filled with 324 ml of water. (a) What is the height of the water level in cm? (b) How many more millilitres of water are 12 cm ? 9 cm needed to fill the tank to its brim? (a) Volume of water = 324 ml = 324 cm3 Height of water level = 324 9 × 9 = 4 cm The height of the water level is 4 cm. (b) Capacity of container = 9 cm × 9 cm × 12 cm = 972 cm3 = 972 ml Amount of water needed = 972 ml – 324 ml = 648 ml 648 ml of water is needed to fill the tank to its brim. watch me
CHAPTER 8 Volume of cubes and cuboids 189 A rectangular tank measuring 30 cm × 24 cm × 12 cm contains 3.6 l of water. (a) Find the height of the water level in cm. (b) Find the amount of water needed to fill the tank completely. Give your answer in litres and millilitres. 12 cm 24 cm 30 cm (a) Volume of water = 3.6 l = cm3 Height of water level = × = cm The height of the water level is cm. (b) Capacity of tank = cm × cm × cm = cm3 = ml Amount of water needed = ml – ml = ml = l ml l ml of water is needed to fill the tank completely.
190 Mathematics Grade 5 A rectangular container measuring 20 cm by 15 cm by 30 cm is 1 2 full of water. What is the volume of water in the container? Give your answer in litres. (1 l = 100 cm3 ) 30 cm 15 cm 20 cm Height of water level = 1 2 × 30 cm = 15 cm Volume of water = 20 cm × 15 cm × 15 cm = 4500 cm3 = 4500 ml = 4.5 l The volume of water in the container is 4.5 l. A rectangular tank measuring 32 cm by 12 cm by 24 cm is 1 3 full of water. How much more water is needed to fill the tank completely? Give your answer in l and ml. (1 l = 1000 cm3 ) Height of water level = × = cm Volume of water = cm × cm × cm = cm3 = ml Capacity of tank = cm × cm × cm = cm3 = ml Volume of water needed = – = ml = l ml l ml of water is needed to fill the tank completely. 24 cm 12 cm 32 cm
CHAPTER 8 Volume of cubes and cuboids 191 A rectangular container has a height of 30 cm. It also has a square base. The container is completely filled when 4.32 l of water is poured into it. What is the length of one edge of the base? (1 l = 1000 cm3 ) Give your answer in cm. Volume of water = Area of base × Height 30 cm ? Area of base × 30 cm = 4320 cm3 Area of base = 4320 cm3 ÷ 30 cm = 144 cm2 Edge of base = 144 = 12 cm The length of one edge of the base is 12 cm. A rectangular tank has square faces and it is of length 25 cm. The capacity of the tank is 5625 ml. Find the length of one edge of each square face. (1 l = 1000 cm3 ) Capacity of tank = Area of square face × Area of square face × cm = ml = cm3 Area of square face = cm3 ÷ cm = cm2 Length of one edge = = cm The length of one edge of each square face is cm. 4.32 l = 4320 ml = 4320 cm3 ? 25 cm
