96 Mathematics Grade 5 6. A train travels at a speed of 80 km/h. How long will it take to travel a distance of 300 km? 7. A bus travelled from Town A to Town B at a speed of 120 km/h. The bus left Town A at 7.40 a.m. and reached Town B at 1.25 p.m. on the same day. What is the distance between Town A and Town B? B Complete the table below. Distance Time taken Speed (Distance ÷ Time) 1. 546 km 3 h 2. 72 m 12 m/s 3. 20 min 95 m/min 4. 450 cm 15 s 5. 17 h 215 km/h 6. 1512 m 56 m/min 7. 2208 m 69 s 8. 3348 km 108 km/h 80 km = 1 h 300 km = 300 80 = 15 4 = 3 3 4 h = 3 h + 3 4 h= 3 h 45 min Total time taken = 5 h + 20 min + 25 min = 5 h + 45 min = 5 h + 3 4 h = 5 3 4 h 3 h 45 min 690 km 182 6 s 1900 m 3655 km 30 cm/s 32 m/s 27 min 31 h Speed = 120 km/h Distance = 120 × 5 3 4 = 120 × 23 4 = 690 km 1 30 15 4 For Teachers Only
97 Chapter 7 Speed C Find the average speed. 1. Distance Time taken A B C 40 cm 20 s 30 s 60 cm The snail’s average speed for the whole journey was . 2. Distance Time taken X Y Z 180 km 2 h 3 h 325 km The average speed of the car for the whole journey was . 3. Distance Time taken P Q R 240 m 68 s 74 s 186 m The horse’s average speed for the whole journey was . Total distance = 40 cm + 60 cm = 100 cm Time taken = 20 s + 30 s = 50 s Total distance = 180 km + 325 km = 505 km Time taken = 2 h + 3 h = 5 h Total distance = 240 m + 186 m = 426 m Time taken = 68 s + 74 s = 142 s Average speed = 100 cm 50 s = 2 cm/s Average speed = 505 km 5 h = 101 km/h Average speed = 426 m 142 s = 3 m/s 2 cm/s 101 km/h 3 m/s 1 101 3 1 1 2 For Teachers Only
98 Mathematics Grade 5 4. Distance Time taken D E F 30 min 3 h 497 km 2485 km The average speed of the aeroplane for the whole journey was . 5. Distance Time taken K L M N 3140 m 36 min 15 min 11 min 1462 m 978 m The average speed of the bicycle for the whole journey was . 6. Distance Time taken E F G H 43 km 37 min 12 min 26 min 16 km 31 km The average speed of the train for the whole journey was . Total distance = 497 km + 2485 km = 2982 km Time taken = 3 h 30 min = 3 h + 1 2 h = 3 1 2 h = 7 2 h Total distance = 3140 m + 1462 m + 978 m = 5580 m Time taken = 36 min + 15 min + 11 min = 62 min Total distance = 43 km + 16 km + 31 km = 90 km Time taken = 37 min + 12 min + 26 min = 75 min Average speed = 5580 m 62 min = 90 m/min Average speed = 90 m 75 min = 1.2 km/min 90 m/min 1.2 km/min Average speed = 2982 km ÷ 7 2 h = 2982 km × 2 7 h = 852 km/h 1 426 852 km/h 18 15 5 6 For Teachers Only
99 Chapter 7 Speed D Write your answers on the lines provided. 1. An athlete ran 1210 m in 5 minutes. What was the athlete’s running speed? 2. Mrs Rajes drove her car at a speed of 95 km/h. How long would she take to travel a distance of 190 km? 3. Eugene started walking to his school at 6.40 a.m. The distance between his house and his school is 600 m. If Eugene reached his school at 6.55 a.m., find his speed. Speed = Distance ÷ Time = 1210 m ÷ 5 min = 242 m/min Time = Distance ÷ Speed = 190 km ÷ 95 km/h = 2 h Time taken = 15 min Distance = 600 m Speed = Distance ÷ Time = 600 m ÷ 15 min = 40 m/min 242 m/min 2 h 40 m/min 6.40 a.m. 6.55 a.m. 15 min For Teachers Only
100 Mathematics Grade 5 4. A plane travelled at a speed of 280 m/s for the first 10 minutes. It then travelled at a speed of 163 m/s for 3 minutes. Find the total distance that the plane travelled. 5. Evelyn started jogging to her friend’s house at 8.37 a.m. She jogged a distance of 3360 m at a speed of 120 m/min. At what time did Evelyn reach her friend’s house? 6. Aaron took 1 3 h to travel 35 km. He travelled the remaining 3 4 of the journey in 5 6 h. Find Aaron’s average speed for the whole distance. 1 min = 60 s 10 min = 10 × 60 = 600 s 280 m/s × 600 s = 168 000 m 3 min = 3 × 60 s = 180 s 163 m/s × 180 s = 29 340 m Total distance = 168 000 m + 29 340 m = 197 340 m 1st part of journey = 35 km 2nd part of journey = 3 × 35 km = 105 km Total distance = 35 km + 105 km = 140 km Time taken = 1 3 h + 5 6 h = 2 6 h + 5 6 h = 7 6 h Time = Distance ÷ Speed = 3360 m ÷ 120 m/min = 28 min 197 340 m 9.05 a.m. 120 km/h 28 min after 8.37 a.m. is 9.05 a.m. 23 min 5 min 8.37 a.m. 9.00 a.m. 9.05 a.m. Average speed = 140 km ÷ 7 6 h = 140 km × 6 7 h = 120 km/h 1 20 For Teachers Only
101 Chapter 7 Speed E Solve the following word problems. 1. The distance between City X and City Y is 275 km. Bill travels from City X to City Y at an average speed of 110 km/h. If he starts his trip at 11.20 a.m., at what time will he reach City Y? 2. Jim can run 10 laps of a 400 m track in 1 3 h. Find Jim’s average speed. Give your answer in m/min. 3. Susan took 2 1 2 h to travel 3 8 of the journey between Town A and Town B at an average speed of 96 km/h. If she took 6 2 5 h to travel from Town A to Town B, find Susan’s average speed. Distance = 275 km Speed = 110 km/h Time taken = 275 km ÷ 110 km/h = 2.5 h = 2 h 30 min 2 h 30 min after 11.20 a.m. is 1.50 p.m. Bill will reach City Y at 1.50 p.m. Total distance = 10 × 400 m = 4000 m Time taken = 1 3 h = 1 3 × 60 min = 20 min 1 h 11.20 a.m. 12.20 p.m. 1.20 p.m. 1.50 p.m. 1 h 30 min Average speed = 4000 m 20 min = 200 m/min Jim’s average speed is 200 m/min. Average speed = 640 km ÷ 6 2 5 h = 640 km × 5 32 h = 100 km/h Susan’s average speed was 100 km/h. 200 1 Distance = 96 km/h × 2 1 2 h = 96 km × 5 2 h = 240 km 3 8 = 3 units 3 units 240 km 1 unit 240 km ÷ 3 = 80 km Total distance = 8 × 80 km = 640 km 20 1 48 1 80 4 1 20 For Teachers Only
102 Mathematics Grade 5 4. May and June drove from their office to a restaurant along the same route. May drove at a speed of 81 km/h and took 20 minutes to reach the restaurant. If June reached the restaurant in 18 minutes, find the difference in their driving speed. 5. Matt travelled at a speed of 80 km/h for the first 4 9 of his journey. He then travelled the remaining journey in 40 minutes at a speed of 90 km/h. How much time did Matt take to travel the entire journey? Give your answer in hours and minutes. 20 min = 20 60 = 1 3 h Distance = 81 km/h × 1 3 h = 27 km 18 min = 18 60 = 3 10 2nd part of journey = 1 – 4 9 = 5 9 40 min = 40 60 = 2 3 h Distance = 90 km/h × 2 3 h = 60 km 5 9 = 5 units 5 units 60 km 1 unit 60 km ÷ 5 = 12 km Total distance = 9 units 9 units 9 × 12 km = 108 km Speed = 27 km ÷ 3 10 h = 27 km × 10 3 h = 90 km/h 1 27 1 3 3 10 1st part of journey = 4 9 × 108 km = 48 km 48 km 80 km/h = 3 5 h 3 5 × 60 min = 36 min Total time taken = 36 min + 40 min = 76 min = 60 min + 16 min = 1 h 16 min Matt took 1 h 16 min to travel the entire journey. June’s driving speed was 90 km/h. 90 km/h – 81 km/h = 9 km/h The difference in their driving speed was 9 km/h. 9 1 2 3 30 1 12 1 3 6 5 10 12 1 For Teachers Only
103 Chapter 7 Speed 6. David and Tom drove from Village P to Village Q at an average speed of 80 km/h and 64 km/h respectively. Both of them took the same route and reached Village Q at 3 p.m. If David left Village P at 12 noon, at what time did Tom leave Village P? 7. Mr Ken left his house at 6.10 a.m. He drove at an average speed of 72 km/h and reached his school at 7 a.m. If Mr Ken increased his speed to 90 km/h, at what time should he leave his house so that he could reach his school at the same time? Time taken = 3 h Speed = 80 km/h Distance = 3 h × 80 km/h = 240 km The distance between Village P and Village Q is 240 km. 240 km 64 km/h = 15 4 h = 3 3 4 h = 3h + = 3 4 h = 3h + 45 min = 3h 45 min 3 h 45 min before 3 p.m. is 11.15 a.m. Tom left Village P at 11.15 a.m. Time taken = 50 min 50 60 = 5 6 h Speed = 72 km/h Distance = 72 × 5 6 h = 60 km The distance between Mr Ken’s house and his school is 60 km. Speed = 90 km/h Distance = 60 m Time taken = 60 km/h 90 km/h = 2 3 h = 40 min 40 min before 7.00 a.m. is 6.20 a.m. He should leave his house at 6.20 a.m. 1 h 1 h 1 h 12 noon 1 p.m. 2 p.m. 3 p.m. 45 min 3 h 11.15 a.m. 12 noon 3 p.m. 3 2 1 12 30 8 15 4 50 min 6.10 a.m. 7 a.m. 10 min 30 min 6.20 a.m. 6.30 a.m. 7.00 a.m. For Teachers Only
104 Mathematics Grade 5 8. Emily and Dorothy left Town A at 2.40 p.m. Their average speeds were 70 km/h and 63 km/h respectively. If Emily reached Town B at 3.28 p.m., how far away was Dorothy from Town B? 9. Zack left his house at 8.15 a.m. He walked at an average speed of 75 m/ min to a shop 900 m away from his house. He rested for 30 minutes at the shop. He then walked at an average speed of 80 m/min to the library which is 1.2 km away from the shop. At what time did Zack reach the library? Emily took 48 min to travel from Town A to Town B. 48 min = 48 60 = 4 5 h 4 5 h × 70 km/h = 56 km The distance between Town A and Town B is 56 km. 4 5 h × 63 km/h = 252 km 5 = 50.4 km Dorothy travelled 50.4 km. 56 km – 50.4 km = 5.6 km Dorothy was 5.6 km away from Town B. Time taken = 900 m 75 m/min = 12 min 12 min after 8.15 a.m. is 8.27 a.m. Zack reached the shop at 8.27 a.m. 30 min after 8.27 a.m. is 8.57 a.m. Zack left the shop at 8.57 a.m. 1.2 km = 1.2 × 1000 = 1200 m Time taken = 1200 m 80 m/min = 15 min 15 min after 8.57 a.m. is 9.12 a.m. Zack reached the library at 9.12 a.m. 1 14 15 1 20 min 28 min 2.40 p.m. 3.00 p.m. 3.28 p.m. 12 min 8.15 a.m. 8.27 a.m. 30 min 8.27 a.m. 8.57 a.m. 3 min 12 min 8.57 a.m. 9.00 a.m. 9.12 a.m. 5 4 For Teachers Only
105 Chapter 7 Speed A 1 m/s C 2 m/s B 1 1 —2 m/s D 2 1 —2 m/s 6. A car is travelling at a speed of 76 km/h. how far can it travel in 2 3 —4 h? A 190 km C 209 km B 195 km D 228 km 7. A bicycle travels at an average speed of 30 km/h. In 7 hours, the distance travelled by the bicycle is A 250 km C 220 km B 210 km D 240 km 8. A train is travelling from Station P to Station Q at an average speed of 90 km/h. The train leaves Station P at 10.00 a.m. Given that the distance between Station P and Station Q is 120 km, at what time will the train reach Station Q? A 11.00 a.m. C 11.40 a.m. B 11.20 a.m. D 12.00 p.m. 9. Idris took part in a 200 metre running race. He ran the first 100 m in 13 seconds and the rest of the distance in 12 seconds. What is the average speed of Idris? Circle the correct answer. 1. What is the formula to calculate average speed? A Distance × Time B Time ÷ Distance C Distance ÷ Time D Speed × 1 —2 2. All of the following are units of speed except A m/min C m/s B km/h D h/min 3. A car travelled at a speed of 120 km/h from Town M to Town N in 5 hours. What is the distance between Town M and Town N? A 24 km C 60 km B 240 km D 600 km 4. Joey walks to school everyday at a speed of 120 m/min. The distance between her house and the school is 960 m. How long does Joey take to walk from her house to school? A 4 minutes C 8 minutes B 6 minutes D 10 minutes 5. Mr Sugianto is jogging. He jogs a distance of 300 m in 120 s. What is his jogging speed? Mastery Practice For Teachers Only
106 Mathematics Grade 5 A 4 m/s C 12 m/s B 8 m/s D 13 m/s 10. Adi swam for 100 seconds at a speed of 1.5 m/s. He then swam for another 150 m. If he took 200 seconds in total to complete the swim, What was his average speed? A 1 m/s C 2 m/s B 1.5 m/s D 2.5 m/s 11. Mdm Lee drove from City P to City Q. She travelled a distance of 360 km at a speed of 90 km/h. If Mdm Lee left City P at 11.00 a.m, what time did she reach City Q? A 1.00 p.m C 3.00 p.m B 2.00 p.m D 4.00 p.m 12. Kenny threw a ball to Mina. The ball travelled at a speed of 60 cm/s and reached Mina in 2 s. Mina threw the ball back to Kenny at the speed of 50 cm/s. How long did it took for the ball to reach Kenny? A 2 s C 2.4 s B 2.8 s D 3 s 13. The distance between State J and State K is 600 km. A bus travelled the first 120 km at a speed of 80 km/h. If the bus took a total of 6.5 hours to reach State K, find its average speed for the remaining journey. A 96 km/h C 100 km/h B 120 km/h D 200 km/h 14. Andy took 30 minutes to drive from his house to the airport. The distance between his house and the airport is 54 km. Find his speed. A 1.8 km/h C 180 km/h B 108 km/h D 54 km/h For Teachers Only
Chapter 8 Volume of cubes and cuboids 107 Chapter 8 Volume of cubes and cuboids Volume of cuboid and cube 1 millilitre (ml) = 1 cubic centimetre (cm3 ) 1 litre (l) = 1000 millilitres (ml) = 1000 cubic centimetres (cm3 ) 1 cubic metre (m3 ) = 1000 litres (l) 1 cubic metre (m3 ) = 1 000 000 cubic centimetres (cm3 ) Volume of cuboid = Length × Breadth × Height Volume of cube = Edge × Edge × Edge Height Breadth Length Edge For Teachers Only
Mathematics Grade 5 108 A How many unit cubes are used to build each solid? Fill in each blank with the correct answer. 1. 2. Number of unit cubes = Number of unit cubes = 3. 4. Number of unit cubes = Number of unit cubes = 5. 6. Number of unit cubes = Number of unit cubes = Exercises 7 15 19 11 25 21 For Teachers Only
109 Chapter 8 Volume of cubes and cuboids B Draw the following solids on a the dot grid provided. 1. 2. 3. 4. For Teachers Only
110 Mathematics Grade 5 C Complete the drawing of each cube or cuboid. 1. 2. 3. 4. 5. 6. For Teachers Only
111 Chapter 8 Volume of cubes and cuboids D These solids are made up of unit cubes. Find the volume of each solid. 1. 2. Volume = cubic units Volume = cubic units 3. 4. Volume = cubic units Volume = cubic units E These solids are made up of 1-cm cubes. Find the volume of each solid. 1. 2. Volume = cm3 Volume = cm3 3. 4. Volume = cm3 Volume = cm3 12 27 7 20 9 11 14 12 For Teachers Only
112 Mathematics Grade 5 F The following solids are made up of 1-cm cubes. Fill in each blank with the correct answer. 1. Height Length Breadth Length = cm Breadth= cm Height = cm Volume = cm3 2. Height Length Breadth Length = cm Breadth= cm Height = cm Volume = cm3 3. Height Breadth Length Length = cm Breadth= cm Height = cm Volume = cm3 4. Height Breadth Length Length = cm Breadth= cm Height = cm Volume = cm3 3 2 6 5 3 2 4 2 3 6 1 6 27 24 24 60 For Teachers Only
113 Chapter 8 Volume of cubes and cuboids G Find the volume of each solid below. 1. 7 cm 3 cm 10 cm Length = cm Breadth= cm Height = cm Volume = cm × cm × cm = cm3 2. 8 cm 8 cm 8 cm Edge = cm Volume = cm × cm × cm = cm3 3. 13 cm 20 cm 25 cm Length = cm Breadth= cm Height = cm Volume = cm × cm × cm = cm3 4. 12 cm 12 cm 12 cm Edge = cm Volume = cm × cm × cm = cm3 10 3 7 10 8 512 20 13 25 20 13 25 6500 12 12 1728 12 12 8 8 3 7 210 8 For Teachers Only
114 Mathematics Grade 5 H Express the following in cubic centimetres. 1. 28 ml = cm3 2. 526 ml = cm3 3. 2 l 45 ml = cm3 4. 35 l 120 ml = cm3 5. 43 l 208 ml = cm3 6. 15 l 35 ml = cm3 7. 1245 ml = cm3 8. 7503 ml = cm3 I Fill in the correct answer in each blank. 1. 73 cm3 = ml 2. 485 cm3 = l ml 3. 3726 cm3 = l ml 4. 8010 cm3 = l ml 5. 26 058 cm3 = l ml 6. 53 800 cm3 = l ml 7. 1893 cm3 = l ml 8. 98 002 cm3 = l ml J Solve the following word problems. 1. A rectangular tank measures 22 cm by 14 cm by 17 cm. Find the volume of water in the tank when the water level reaches 7 cm below its brim. 28 2045 43 208 1245 73 3 26 1 98 53 726 8 58 893 2 800 10 485 7503 15 035 35 120 526 17 cm – 7 cm = 10 cm The water level of the tank is 10 cm. Volume = 22 cm × 14 cm × 10 cm = 3080 cm3 The volume of water in the tank is 3080 cm3 . For Teachers Only
115 Chapter 8 Volume of cubes and cuboids 2. Find the volume of a cube of edges 15 cm. 3. A rectangular tank 30 cm by 50 cm by 60 cm is 60% filled with water. All the water is poured into another rectangular container with a square base of side 20 cm and 140 cm height. What is the level of water in the second container? 4. A container measures 15 cm by 20 cm by 5 cm. A 300-ml cup filled with water is used to fill the container to its brim. How many cups of water are needed to fill the container completely? Volume = 15 cm × 15 cm × 15 cm = 3375 cm3 The volume of the cube is 3375 cm3 . 15 cm × 20 cm × 5 cm = 1500 cm3 The volume of the container is 1500 cm3 . 300 ml = 300 cm3 The volume of the cup is 300 cm3 . 1500 cm3 ÷ 300 cm3 = 5 5 cups of water are needed to fill the container completely. Volume = 30 cm × 50 cm × 60 cm = 90 000 cm3 The volume of the rectangular tank is 90 000 cm3 . 60% = 60 100 60 100 × 90 000 cm3 = 54 000 cm3 The volume of water in the tank is 54 000 cm3 . 20 cm × 20 cm × Height = 54 000 cm3 400 cm3 × Height = 54 000 cm3 Height = 54 000 cm ÷ 400 cm3 = 135 cm The level of water in the second container is 135 cm. 30 cm 50 cm 60 cm ? 140 cm 20 cm 20 cm For Teachers Only
116 Mathematics Grade 5 5. A tank 40 cm by 28 cm by 30 cm is 3 5 filled with water. How much more water is needed to fill the tank completely? Give your answer in litres. (1 l = 1000 cm3 ) 6. A rectangular tank 25 cm long, 28 cm wide and 12 cm high is completely filled with water. Then, 40% of the water from the tank is used up. (a) How much water is left in the tank? Give your answer in litres and millilitres. (1 l = 1000 cm3 ) (b) Find the level of water left in the tank. 40 cm × 28 cm × 30 cm = 33 600 cm3 The volume of the tank is 33 600 cm3 . 3 5 × 33 600 cm3 = 20 160 cm3 The volume of water in the tank is 20 160 cm3 . 33 600 cm3 – 20 160 cm3 = 13 440 cm3 13 440 cm3 = 13 440 ml = 13 000 ml + 440 ml = 13 l + 440 ml = 13 l 440 ml = 13.440 l 13.44 l more water is needed to fill the tank completely. (a) 25 cm × 28 cm × 12 cm = 8400 cm3 The volume of the tank is 8400 cm3 . 100% – 40% = 60% 60% of water is left in the tank. 60 100 × 8400 cm3 = 5040 cm3 5040 cm3 = 5040 ml = 5000 ml + 40 ml = 5 l 40 ml 5 l 40 ml of water is left in the tank. (b)25 cm × 28 cm × Height = 5040 cm3 700 cm2 × Height = 5040 cm3 Height = 5040 cm3 ÷ 700 cm2 = 7.2 cm The level of water left in the tank is 7.2 cm. 1 6720 For Teachers Only
117 Chapter 8 Volume of cubes and cuboids 7. An empty tank 70 cm long, 20 cm wide and 10 cm high. Water from tap flows into the tank at a constant rate of 1 2 l per minute. How long does it take for the water to reach the brim of the tank? (1 l = 1000 cm3 ) 8. Carton A measures 15 cm by 24 cm by 18 cm. Carton B has edges 17 cm long. Find the difference in capacities between Carton A and Carton B. 70 cm × 20 cm × 10 cm = 14 000 cm3 The volume of the tank is 14 000 cm3 . 1 2 l = 0.5 l = 500 ml = 500 cm3 14 000 cm3 ÷ 500 cm3 = 28 28 minutes is needed for the water to reach the brim of the tank. 15 cm × 24 cm × 18 cm = 6480 cm3 The volume of Carton A is 6480 cm3 . 17 cm × 17 cm × 17 cm = 4913 cm3 The volume of Carton B is 4913 cm3 . 6480 cm3 – 4913 cm3 = 1567 cm3 The difference in capacities between Carton A and Carton B is 1567 cm3 . For Teachers Only
118 Mathematics Grade 5 K Find the square roots of the following numbers. 1. 81 = 2. 100 = 3. 121 = 4. 144 = 5. 169 = 6. 2 25 = 7. 400 = 8. 625 = 9. 900 = 10. 1600 = L Find the cube roots of the following numbers. 1. 3 216 = 2. 3 343 = 3. 3 512 = 4. 3 729 = 5. 3 1331 = 6. 3 1000 = 7. 3 1728 = 8. 3 2197 = 9. 3 3575 = 10. 3 2744 = 9 10 11 12 13 15 20 25 30 6 7 9 10 13 14 8 11 12 15 40 For Teachers Only
119 Chapter 8 Volume of cubes and cuboids M Find the volume of each solid. 1. 4 cm 4 cm 4 cm Volume = cm × cm × cm = cm3 2. 8 cm 4 cm 3 cm Volume = cm × cm × cm = cm3 3. 10 cm 5 cm 6 cm Volume = cm × cm × cm = cm3 4. 10 cm 6 cm 6 cm Volume = cm × cm × cm = cm3 4 8 6 6 4 4 5 10 4 3 10 6 64 96 300 360 For Teachers Only
120 Mathematics Grade 5 N Find the volume of water in each of the following tank. Give your answer in litres correct to 1 decimal place. (1l = 1000 cm3 ) 1. Length = cm Breadth = cm Height of solid = cm – cm = cm Volume = cm × cm × cm = cm3 = l 2. Length = Breadth = Height = Volume = 9 cm 2 cm 11 cm 7 cm 50 cm 30 cm 20 cm 20 cm 11 11 7 7 7 539 0.5 30 cm 20 cm 50 cm – 20 cm = 30 cm 30 cm × 20 cm × 30 cm = 18 000 cm3 ÷ 1000 = 18 l 9 7 2 For Teachers Only
121 Chapter 8 Volume of cubes and cuboids 3. 18 cm 9 cm 22 cm 16 cm Length = Breadth = Height = Volume = 4. 15 cm 13 cm 10 cm 10 cm Length = Breadth = Height = Volume = 18 cm 9 cm 22 cm – 16 cm = 6 cm 18 cm × 9 cm × 6 cm = 972 cm3 ÷ 1000 = 1 l 10 cm 10 cm 13 cm 10 cm × 10 cm × 13 cm = 13 000 cm3 ÷ 1000 = 1.3 l For Teachers Only
122 Mathematics Grade 5 O Find the unknown edge of each solid. 1. The volume of a cube is 125 cm3 . What is the length of each edge? 2. The solid shown is a cube. The area of the shaded face is 144 cm2 . Find the length of its edge. 3. 5 cm 7 cm ? Height The volume of a cuboid is 315 cm3 . Find its height. 4. x cm The volume of the cuboid is 2024 cm3 . The area of the shaded face is 253 cm2 . Find the value of x. Volume of cube = 125 cm3 Length of each edge = 3 125 = 5 × 5 × 5 = 5 cm Area of square = 144 cm2 Length of edge = 144 = 12 × 12 = 12 cm Height × 5 cm × 7 cm = 315 cm3 Height = 315 5 × 7 = 9 cm Area of shaded face = 253 cm2 Volume of cuboid = 2024 cm3 2024 cm3 = 253 cm2 × x x = 2024 cm3 253 cm3 = 8 cm For Teachers Only
123 Chapter 8 Volume of cubes and cuboids P Write your answers on the lines provided. 1. A largest possible square block is cut from the solid shown below. Find the volume of the remaining block. 17 cm 21 cm 18 cm 2. A tank with a square base area of 625 cm2 has a capacity of 21.25 l. Find the height of the tank. 625 cm2 ? Height Volume of largest possible square block = 17 cm × 17 cm × 17 cm = 4913 cm3 Volume of solid = 18 cm × 17 cm × 21 cm = 6426 cm3 6426 cm3 – 4913 cm3 = 1513 cm3 21.25 l = 21 250 ml = 21 250 cm3 Area of square base = 625 cm2 Height of tank = 21 250 625 = 34 cm 1513 cm3 34 cm For Teachers Only
124 Mathematics Grade 5 3. How much water is needed to fill the tank to its brim? Give your answer in l. 30 cm 21 cm 23 cm 18 cm 4. The length of Cube P is thrice the length of Cube Q. Find the ratio of the volume of Cube P to the volume of Cube Q. Cube P Cube Q Height of water level of additional volume of water = 30 cm – 21 cm = 9 cm Volume of water needed to fill the tank to its brim = 23 cm × 18 cm × 9 cm = 3726 cm3 = 3726 ml ÷ 100 = 3.726 l Length of Cube P : Length of Cube Q 3 : 1 Volume of a cube = Length × Breadth × Height Volume of Cube P : Volume of Cube Q (3 × 3 × 3) : (1 × 1 × 1) 27 : 1 3.726 l 27 : 1 For Teachers Only
125 Chapter 8 Volume of cubes and cuboids 5. 14 identical cubes with edges of 5 cm are glued together to form a solid as shown below. If the top layer is removed, what is the total volume of the remaining solid? 6. A tank with a square base is 2 3 full of water. The water is then poured into a cubical tank to fill it completely. What is the length of each edge of the cubical tank? ? cm ? cm ? cm 1375 cm3 18 cm Total number of cubes = 14 Remaining cubes = 14 – 3 = 11 Volume of the remaining cubes = 11 × (5 cm × 5 cm × 5 cm) = 11 × 125 cm3 = 1375 cm3 Volume of water = 2 3 × 18 cm × 18 cm × 27 cm = 2 cm × 6 cm × 18 cm × 27 cm = 5832 cm3 Length of each edge of cubical tank = 3 5832 = 18 × 18 × 18 = 18 cm 6 1 For Teachers Only
126 Mathematics Grade 5 7. A rectangular tank measuring 32 cm by 25 cm by 18 cm. Water flows into the tank at the rate of 0.9 l per minute. How long will it take to fill up the tank to its brim? 8. Tank A is completely filled with water. The water is then poured into an empty rectangular Tank B, find the height of the water level in the tank. 35 cm 40 cm 18 cm 21 cm Tank A Tank B 441 cm2 Volume of tank = 32 cm × 25 cm × 18 cm = 14 400 cm3 = 14 400 ml ÷ 1000 = 14.4 l 0.9 l = 1 min Time taken = 14.4 0.9 = 144 9 = 16 min Volume of water in Tank A = 21 cm × 18 cm × 35 cm = 13 230 cm3 Area of base for Tank B = 441 cm2 Height of the water level in Tank B = 13 230 441 = 30 cm 16 min 30 cm 48 16 1 3 For Teachers Only
127 Chapter 8 Volume of cubes and cuboids Q Solve the following word problems. 1. Tank X is 1 2 full of water while Tank Y is 2 3 full of water. Both tanks contain the same amount of water. (a) Find the height of the water level in Tank Y. (b) Find the height of Tank Y. 10 cm 4 cm 12 cm ? Height 6 cm 5 cm Tank X Tank Y (a) Volume of water in Tank X = 1 2 × 12 cm × 4 cm × 10 cm = 6 cm × 4 cm × 10 cm = 240 cm3 Tank X contains 240 cm3 of water. Height of water level in Tank Y = 240 5 × 6 = 8 cm The height of water level in Tank Y is 8 cm. (b) 2 3 = 8 cm 2 units 8 cm 1 unit 8 2 = 4 cm 3 units 3 × 4 cm = 12 cm The height of Tank Y is 12 cm. 6 1 For Teachers Only
128 Mathematics Grade 5 2. A rectangular tank measuring 26 cm by 18 cm by 30 cm contains 3.51 l of water. (a) What percentage of the capacity of the tank is filled with water? (b) How much more water is needed to fill up the tank? Give your answer in litres. 3. An empty rectangular tank measures 120 cm by 160 cm by 210 cm. Water flows into the tank at 36 l per minute. (a) How many minutes will it take to fill the whole tank with water? (b) If the water leaks out at 8 l per minute at the same time, how much longer will it take to fill up the tank? (a) Volume of tank = 26 cm × 18 cm × 30 cm = 14 040 cm3 3.51 l = 3.51 l × 1000 = 3510 ml = 3510 cm3 3510 14 040 × 100% = 25% 25% of the tank is filled with water. (b) 14 040 cm3 – 3510 cm3 = 10 530 cm3 = 10 530 ml ÷ 1000 = 10.53 l 10.53 l of water are need to fill up the tank. (a) Volume of tank = 120 cm × 160 cm × 210 cm = 4 032 000 cm3 = 4 032 000 ml ÷ 1000 = 4032 l 36 l = 1 min Time taken = 4032 36 = 112 min It takes 112 minutes to fill the whole tank with water. (b) Rate of water flow = 36 l per min – 8 l per min = 28 l per min Time taken = 4032 28 = 144 min 144 min – 112 min = 32 min It will take 32 minutes more to fill up the tank. For Teachers Only
129 Chapter 8 Volume of cubes and cuboids 4. The base of a rectangular tank measures 27 cm by 25 cm. It is 50% full of water. If the volume of water in the tank is 18 l 900 ml, (a) Find the height of the tank. (b) All the water is then equally poured into two similar containers with the base area of 450 cm2 . Find the height of the water level of each container. ? Height ? Height ? Height ? Height 25 cm 27 cm 450 cm2 450 cm2 Tank X Tank Y (a) 18 l 900 ml = 18 l + 900 ml = 18 000 ml + 900 ml = 18 900 ml = 18 900 cm3 50% = 18 900 cm3 100% = 2 × 18 900 cm2 = 37 800 cm3 Height of tank = 37 800 27 × 25 = 37 800 675 = 56 cm The height of the tank is 56 cm. (b) 18 900 cm3 2 = 9450 cm3 Each container contains 9450 cm3 of water. Height of water level in each container = 9450 450 = 21 cm The height of water level of each container is 21 cm. 21 1 For Teachers Only
130 Mathematics Grade 5 5. An empty aquarium has a base area of 1690 cm2 . It is filled with water flowing from a tap at 6.5 l per minute. The aquarium is completely filled in 26 m inutes. (a) Find the height of the aquarium. (b) If the aquarium must be completely filled in 1690 cm2 half of the initial time, what should the rate of water flow be? 6. A rectangular tank with a base area of 8000 cm2 contains 112 000 cm3 of water. It is fitted with two taps. Water flows from Tap A into the tank at 3 l per minute. Tap B drains the water out from the tank at 5 l per minute. Both taps are turned on at the same time. (a) What is the height of the water level after 20 minutes? (b) How long will it take to empty the tank? Tap A Tap B (a) 1 min = 6.5 l 26 min = 26 × 6.5 l = 169 l × 1000 = 169 000 ml = 169 000 cm3 The volume of the aquarium = 169 000 1690 = 100 cm The height of the aquarium is 100 cm. (b) 26 min 13 min Rate of water filling the aquarium = 2 × 6.5 l = 13 l The rate of water flow should be 13 l per minute. (a) Volume of water drained out from tank per min = 5 l – 3 l = 2 l × 1000 = 2000 ml = 2000 cm3 Volume of water draining out of tank = 20 × 2000 cm3 = 40 000 cm3 Remaining volume of water = 112 000 cm3 – 40 000 cm3 = 72 000 cm3 Area of base = 8000 cm3 Height of water level = 72 000 8000 = 9 cm The height of water level after 20 minutes is 9 cm. (b) Time taken = 112 000 2000 = 56 min It will take 56 minutes to empty the tank. 9 1 For Teachers Only
131 Chapter 8 Volume of cubes and cuboids What is the volume of the cuboid? A 480 cm3 C 25 cm3 B 96 cm3 D 60 cm3 5. The volume of the cube is 216 cm3 .Find its edge. A 72 cm C 14 cm B 3 cm D 6 cm 6. 600 cm 2 A rectangular tank has a base area 600 cm2 . It has a capacity of 5.4 l. Find its height. A 90 cm C 19 cm B 9 cm D 0.9 cm 7. 10 cm The length of the cuboid is 10 cm. Its volume is 360 cm3 . Find the length of one side of the cuboid. Circle the correct answer. 1. 1 cubic unit What is the volume of the solid shown above? A 6 cubic units B 12 cubic units C 24 cubic units D 36 cubic units 2. 2 cm 2 cm 2 cm What is the volume of the solid shown above? A 10 cm3 B 30 cm3 C 240 cm3 D 300 cm3 3. 10 cm 5 cm 3 cm What is the capacity of the container? A 18 cm3 C 100 cm3 B 80 cm3 D 150 cm3 4. 8 cm 5 cm 12 cm Mastery Practice For Teachers Only
132 Mathematics Grade 5 A 36 cm C 18 cm B 6 cm D 9 cm 8. A plot of land has an area of 150 m2 . If the ground is to be lowered by 3 cm, how much soil needs to be removed? A 0.45 m3 B 4.5 m3 C 45 m3 D 450 m3 9. If 60 litres of water is needed to fill up a tank that is 60 cm long and 50 cm wide, how tall is the tank? A 20 cm B 25 cm C 30 cm D 35 cm 10. A fish tank is 50 centimetres wide, 80 centimetres long and 60 centimetres tall. If Alvin uses a 5-litre jug to fill up the tank with water, how many times does he fill up the jug? A 44 C 48 B 46 D 50 11. A block of wood is 10 cm wide, 12 cm long and 3 cm thick. If 4 of these blocks are stacked together, how much space will they occupy? A 360 cm3 B 720 cm3 C 1.080 cm3 D 1440 cm3 12. A fish tank is 100 cm long and 60 cm wide. If 180 litres of water can only fill half of the fish tank, how tall is the fish tank? A 50 cm B 60 cm C 70 cm D 80 cm 13. A rectangular piece of sponge measures 10 cm by 6.5 cm by 4 cm. If it is cut into 4 equal pieces. What is the volume of each piece? A 55 cm3 B 60 cm3 C 65 cm3 D 70 cm3 14. A metal cube is 5 cm long, 5 cm wide and 5 cm thick. How many such metal cubes can fit into a 1.5 m long by 0.5 m wide by 0.5 m tall box? A 300 B 3000 C 30 000 D 300 000 15. John has a container which is 2 m long, 1.5 m wide and 3 m tall. He fills 45 blocks of wood of 50 cm long, 100 cm wide and 20 cm tall each into the container. How much empty space is left in the container? A 9 m3 C 4.5 m3 B 5 m3 D 4 m3 For Teachers Only
Chapter 9 Introduction to statistics 133 Chapter 9 Introduction to statistics A Stanley uses tallies to record the number of different types of vegetables he saw in a garden. Study the table below and answer the following questions. IIII IIII IIII IIII IIII IIII IIII III IIII IIII IIII IIII IIII IIII I IIII IIII IIII IIII II IIII IIII IIII II Count the tallies and complete the table below. Types of vegetables Chilli Tomato Courgette Aubergine Number of vegetables Use the table to answer the following questions. 1. Which type of vegetable did Stanley see most in the garden? 2. There are 9 more than . 3. Stanley forgot to record the number of carrots. If there are twice as many carrots as aubergines, how many carrots are there? 4. How many vegetables are there altogether in the garden? Exercises Chili tomatoes courgettes 34 142 38 31 22 17 For Teachers Only
134 Mathematics Grade 5 B The table below shows the number of cars sold by a car company during the last 6 months in 2022. Study the information given and answer the following questions. Month Jul Aug Sept Oct Nov Dec Number of cars sold 15 30 45 20 ? 100 1. If there is a total of 275 cars sold during the last 6 months, how many cars were sold in November? 2. Which month is the most popular month for car buyers? 3. The number of cars sold in is three times as many as the number of cars sold in . 4. The number of cars sold in is twice as many as the number of cars sold in . 5. What is the biggest difference in sales of cars? In which two months did it occur? , 6. Complete the graph below with the data in the table above. 10 0 20 30 40 50 60 70 80 90 100 Jul Aug Sept Oct Nov Dec Month Number of cars sold Number of cars sold from July to December 65 December September July August July July December For Teachers Only
135 Chapter 9 Introduction to statistics C The bar graph below shows the daily profit of a dessert stall from Monday to Saturday. 200 000 Mon Tue Wed Thu Fri Sat 0 400 000 600 000 800 000 1 000 000 Day Profit (Rp) Amount of profit earned by a dessert stall Using data from the bar graph above, complete the following table. Day Monday Tuesday Wednesday Thursday Friday Saturday Profit earned (Rp) Use the table above to answer the following questions. 1. On which day was the greatest profit earned? 2. On which day was the least profit earned? 3. On which two days the dessert stall earned the same amount of profit? 4. On which day the dessert stall earned twice as much profit as on Saturday? Monday Saturday Tuesday and Thursday Wednesday 900 000 600 000 800 000 600 000 500 000 400 000 For Teachers Only
136 Mathematics Grade 5 D Answer the questions based on the given line graphs. 1. The following line graph shows the ages of the winners of the best actress award from 2016 to 2021. 50 60 30 70 80 Age (years) 10 20 0 40 2016 2017 2018 2019 2020 2021 Year Ages of best actress award winners (a) In which year was the winner the oldest? How old was she? (b) In which year was the winner the youngest? How old was she? (c) What is the difference in age between the oldest winner and the youngest winner? (d) How old was the winner of the award for 2021? (e) What is the difference in age between the winners of the award for 2016 and 2020? 2018. She was 75 years old. 2017. She was 25 years old. 50 years. 45 years old. 20 years. For Teachers Only
137 Chapter 9 Introduction to statistics 2. The following line graph shows Mark’s food expenses from Monday to Friday. Amount spend (Rp) 10 000 20 000 30 000 40 000 50 000 60 000 70 000 0 Mon Tue Wed Thu Fri Day Mark’s food expenses (a) On which day did Mark spend the most on food? How much money did he spend on food that day? (b) On which day did Mark spend the least on food? How much money did he spend on food that day? (c) What is the difference between the amounts of money that Mark spent on food on Wednesday and Friday? (d) In which days did Mark spend less than Rp 30.000,00 on food? (e) What is Mark's total food expenses from Monday to Friday? Friday. He spent Rp 60.000,00. Wednesday. He spent Rp 20.000,00. Rp 40.000,00. Monday and Wednesday. Rp 195.000,00. For Teachers Only
138 Mathematics Grade 5 3. The following line graph shows the numbers of patrons who watched 4 different types of movies at a cinema in December. 500 0 1000 1500 2000 2500 3000 Number of patrons Documentary Comedy Thriller Science fiction Children’s Types of movies Number of patrons at a cinema (a) Which type of movie is most popular among the patrons? (b) Which type of movie is the least popular among the patrons? (c) How many more patrons watched Science fiction movies than Documentary movies? (d) What is the total number of patrons who watched movies at the cinema in December? (e) Among the patrons who watched Children’s movie, 1321 of them were children. How many adults were there? Science fiction. Documentary. 1500 more. 10 250. 679 adults. For Teachers Only
139 Chapter 9 Introduction to statistics 4. The line graph shows the monthly electricity consumption of a household from March to August in a certain year. 10 0 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 Mar Apr May Jun Jul Aug Electricity (kWh) Monthly electricity consumption Month (a) What is the electricity consumption in May? (b) Which month has the highest electricity consumption? (c) Which month has twice the quantity of electricity consumption of July? (d) What is the total electricity consumption from March to August? 115 kWh. April. June. 730 kWh. For Teachers Only
140 Mathematics Grade 5 E Answer the questions based on the given pie charts. 1. The following pie chart shows the results of a survey on the favourite types of pies of 50 people. Blueberry 40% Pecan 20% Peach 10% Strawberry 30% Favourite types of pies of 50 people (a) Which type of pie is the most popular among the people? How many people likes it? (b) Which type of pie is the least popular among the people? (c) How many people prefer strawberry pie? (d) What is the percentage of the people that like pecan pie? Blueberry pie. 20 people like it. Peach pie is the least popular among the people. 15 people. 20%. For Teachers Only
141 Chapter 9 Introduction to statistics 2. The pie chart below shows the number of books read by a group of pupils during the holidays. 2 books 1 book 50 3 books 1 3 4 books Number of books read (a) The number of pupils who read 4 books was 1 2 of the number of pupils who read 1 book. How many pupils read 4 books? (b) What fraction of the pupils read 4 books? (c) How many pupils were there altogether? (d) How many pupils read 3 books and more? 25 pupils. 1 18 450 pupils. 175 pupils. For Teachers Only
142 Mathematics Grade 5 3. The pie chart below shows the types of board games sold in Great Games Store in a month. Chess 12 Monopoly 15 Clue Risk Scrabble 14 Type of board games sold in a month (a) The number of monopoly games sold was 3 10 of the total number of board games sold. Find the total number of games sold. (b) What percentage of the board games sold was chess? (c) The number of risk games sold was 1 2 of the number of chess sold. How many risk games were sold? (d) How many clue games did he sell? 50. 24%. 6. 3. For Teachers Only
143 Chapter 9 Introduction to statistics 4. The pie chart below shows the number of electronic gadgets sold during an electronics fair. MP3 player Mobile phone 342 Camera 18% Flash drive 32% Number of electronic gadgets sold (a) What percentage of the gadgets sold were mobile phones? (b) What was the total number of electronic gadgets sold at the electronics fair? (c) If 75% of the people who bought flash drives were businessmen, how many businessmen bought flash drives? (d) If 8 19 of the people who bought MP3 players were teenagers, what was the number of teenagers who bought MP3 players? 25%. 1900. 456. 25%. For Teachers Only
144 Mathematics Grade 5 5. What was the total number of loaves of bread sold from the 2nd week to the 3rd week? A 60 C 190 B 90 D 240 Answer questions 6 to 10 based on the line graph below. Month May Steven’s Savings from May to September 0 Amount (× 100 000 rupiah) 5 10 15 20 Jun Jul Aug Sep 6. How much money did Steven save in June? A 500 000 rupiah B 100 000 rupiah C 550 000 rupiah D 750 000 rupiah 7. In which month did Steven save the least amount of money? A May C August B June D September 8. How much more money did Steven save in September than in July? A 75 000 rupiah B 1 500 000 rupiah C 750 000 rupiah D 950 000 rupiah Circle the correct answer. Answer questions 1 to 5 based on the line graph below. 10 0 20 30 40 50 60 1st week 2nd week 3rd week 4th week Number of loaves of bread Week Number of loaves of bread sold by a bakery 1. The greatest number of loaves of bread was sold in the A 1st week C 3rd week B 2nd week D 4th week 2. Which week recorded the lowest sales? A 1st week C 3rd week B 2nd week D 4th week 3. How many fewer loaves of bread were sold in the 4th week than the 1st week? A 105 C 10 B 20 D 15 4. What was the increase in the number of loaves of bread sold from 2nd week to the 3rd week? A 55 C 20 B 25 D 35 Mastery Practice For Teachers Only
145 Chapter 9 Introduction to statistics 9. What is the total amount of money Steven saved from May to September? A 400 000 rupiah B 450 000 rupiah C 4 000 000 rupiah D 4 500 000 rupiah 10. How much did Steven save on average per month? A 750 000 rupiah B 200 000 rupiah C 800 000 rupiah D 900 000 rupiah Answer questions 11 to 15 based on the pie chart given below. Division of 500 Pupils in a School Grade 4 16% Grade 1 19% Grade 2 Grade 3 18% Grade 5 16% Grade 6 15% 11. How many percent of the pupils are in Grade 2? A 13% C 15% B 14% D 16% 12. Which level has the least number of pupils? A Grade 1 B Grade 2 C Grade 5 D Grade 6 13. Which level has the most number of pupils? A Grade 1 B Grade 2 C Grade 3 D Grade 4 14. How many pupils are there in Grade 5? A 70 C 90 B 80 D 100 15. How many more pupils are there in Grade 1 than in Grade 6? A 10 C 20 B 15 D 25 16. The pie chart shows the types of sandwiches sold in Aaron’s cafe on Monday. Types of sandwiches sold Tuna Egg Chicken Sardine 30 egg sandwiches and 50 tuna sandwiches are sold. The number of chicken sandwiches sold was three times as many as the number of sardine sandwiches sold. How many chicken sandwiches were sold? A 10 C 30 B 40 D 50 For Teachers Only
