Page 1 Question:111 The length, breadth and height of a cuboid are 15 cm, 12 cm and 4.5 cm respectively. Its volume is a 243 cm 3 b 405 cm 3 c 810 cm 3 d 603 cm 3 Solution: c 810 cm 3 Volume of the cuboid = l ×b ×h = 15 ×12 ×4. 5 cm 3 = 810 cm 3 Question:112 A cuboid is 12 cm long, 9 cm broad and 8 cm high. Its total surface area is a 864 cm 2 b 552 cm 2 c 432 cm 2 d 276 cm 2 Solution: b 552 cm 2 Total surface area of the cuboid = 2(lb +bh +lh) cm 2 = 2 12 ×9 +8 ×9 +12 ×8 cm 2 = 2(108 +72 +96) cm 2 Question:113 The length, breadth and height of a cuboid are 15 m, 6 m and 5 dm respectively. The lateral surface area of the cuboid is a 45 m 2 b 21 m 2 c 201 m 2 d 90 m 2 Solution: Length of the cuboid, l = 15 m Breadth of the cuboid, b = 6 m Height of the cuboid, h = 5 dm = 0.5 m 1m = 10dm ? Lateral surface area of the cuboid = 2h(l + b) = 2 × 0.5 × 15 +6 = 2 × 0.5 × 21 = 21 cm 2 Hence, the correct answer is option b. Question:114 A beam 9 m long, 40 cm wide and 20 cm high is made up of iron which weighs 50 kg per cubic metre. The weight of the beam is a 27 kg b 48 kg c 36 kg d 56 kg Solution: c 36 kg Length = 9 m Breadth = 40 cm = 0.4 m Height = 20 cm = 0.2 m ? Weight of the beam = volume of the beam ×weight of iron per cubic metre = 9 ×0. 4 ×0. 2 ×50 = 36 kg Question:115 The length of the longest rod that can be placed in a room of dimensions (10 m × 10 m × 5 m) is a 15 m b 16 m c 10v 5 m d 12 m Solution: a 15 m Length of longest rod = diagonal of the room = diagonal of a cuboid = v l 2 +b 2 +h 2 = v 100 +100 +25 m = v 225 m = 15 m Question:116 What is the maximum length of a pencil that can be placed in a rectangular box of dimensions (8 cm × 6 cm × 5 cm)? a 8 cm b 9.5 cm c 19 cm d 11.2 cm ( ) Page 2 Question:111 The length, breadth and height of a cuboid are 15 cm, 12 cm and 4.5 cm respectively. Its volume is a 243 cm 3 b 405 cm 3 c 810 cm 3 d 603 cm 3 Solution: c 810 cm 3 Volume of the cuboid = l ×b ×h = 15 ×12 ×4. 5 cm 3 = 810 cm 3 Question:112 A cuboid is 12 cm long, 9 cm broad and 8 cm high. Its total surface area is a 864 cm 2 b 552 cm 2 c 432 cm 2 d 276 cm 2 Solution: b 552 cm 2 Total surface area of the cuboid = 2(lb +bh +lh) cm 2 = 2 12 ×9 +8 ×9 +12 ×8 cm 2 = 2(108 +72 +96) cm 2 Question:113 The length, breadth and height of a cuboid are 15 m, 6 m and 5 dm respectively. The lateral surface area of the cuboid is a 45 m 2 b 21 m 2 c 201 m 2 d 90 m 2 Solution: Length of the cuboid, l = 15 m Breadth of the cuboid, b = 6 m Height of the cuboid, h = 5 dm = 0.5 m 1m = 10dm ? Lateral surface area of the cuboid = 2h(l + b) = 2 × 0.5 × 15 +6 = 2 × 0.5 × 21 = 21 cm 2 Hence, the correct answer is option b. Question:114 A beam 9 m long, 40 cm wide and 20 cm high is made up of iron which weighs 50 kg per cubic metre. The weight of the beam is a 27 kg b 48 kg c 36 kg d 56 kg Solution: c 36 kg Length = 9 m Breadth = 40 cm = 0.4 m Height = 20 cm = 0.2 m ? Weight of the beam = volume of the beam ×weight of iron per cubic metre = 9 ×0. 4 ×0. 2 ×50 = 36 kg Question:115 The length of the longest rod that can be placed in a room of dimensions (10 m × 10 m × 5 m) is a 15 m b 16 m c 10v 5 m d 12 m Solution: a 15 m Length of longest rod = diagonal of the room = diagonal of a cuboid = v l 2 +b 2 +h 2 = v 100 +100 +25 m = v 225 m = 15 m Question:116 What is the maximum length of a pencil that can be placed in a rectangular box of dimensions (8 cm × 6 cm × 5 cm)? a 8 cm b 9.5 cm c 19 cm d 11.2 cm ( ) Solution: d 11.2 cm Maximum length of the pencil = diagonal of the box = v l 2 +b 2 +h 2 = v 8 2 +6 2 +5 2 cm = v 64 +36 +25 cm = v 125 cm = 11. 2 cm Question:117 The number of planks of dimensions (4 m × 5 m × 2 m) that can be stored in a pit which is 40 m long, 12 m wide and 16 m deep, is a 190 b 192 c 184 d 180 Solution: b 192 Number of planks = volume of the pit volume of 1 plank = 40×12×16 4×5×2 = 7680 40 = 192 Question:118 How many planks of dimensions (5 m × 25 cm × 10 cm) can be stored in a pit which is 20 m long, 6 m wide and 50 cm deep? a 480 b 450 c 320 d 360 Solution: a 480 Length of the pit = 20 m Breadth of the pit = 6 m Height of the pit = 50 cm = 0.5 m Length of the plank = 5m Breadth of the plank = 25 cm = 0.25 m Height of the plank = 10 cm = 0.1 m ? Number of planks = volume of the pit volume of 1 plank = 20×6×0.5 5×0.25×0.1 = 60×1000 125 = 480 Question:119 How many bricks will be required to construct a wall 8 m long, 6 m high and 22.5 cm thick if each brick measures (25 cm × 11.25 cm × 6 cm)? a 4800 b 5600 c 6400 d 5200 Solution: c 6400 Length of the wall = 8 m = 800 cm Breadth of the wall = 6 m = 600 cm Height of the wall = 22.5 cm Length of the brick = 25 cm Breadth of the brick = 11.25 cm Height of the brick = 6 cm ? Number of bricks required = volume of the wall volume of 1 brick = 800×600×22.5 25×11.25×6 = 10800000 1687.5 = 6400 Question:120 How many persons can be accommodated in a dining hall of dimensions (20 m × 15 m × 4.5 m), assuming that each person requires 5 m 3 of air? a 250 b 270 c 320 d 300 Solution: b 270 Number of persons = volume of the hall volume of air required by 1 person = 20×15×4.5 5 = 20 ×3 ×4. 5 = 270 ? 270 persons can be accommodated. Question:121 A river 1.5 m deep and 30 m wide is flowing at the rate of 3 km per hour. The volume of water that runs into the sea per minute is a 2000 m 3 b 2250 m 3 c 2500 m 3 d 2750 m 3 Solution: Page 3 Question:111 The length, breadth and height of a cuboid are 15 cm, 12 cm and 4.5 cm respectively. Its volume is a 243 cm 3 b 405 cm 3 c 810 cm 3 d 603 cm 3 Solution: c 810 cm 3 Volume of the cuboid = l ×b ×h = 15 ×12 ×4. 5 cm 3 = 810 cm 3 Question:112 A cuboid is 12 cm long, 9 cm broad and 8 cm high. Its total surface area is a 864 cm 2 b 552 cm 2 c 432 cm 2 d 276 cm 2 Solution: b 552 cm 2 Total surface area of the cuboid = 2(lb +bh +lh) cm 2 = 2 12 ×9 +8 ×9 +12 ×8 cm 2 = 2(108 +72 +96) cm 2 Question:113 The length, breadth and height of a cuboid are 15 m, 6 m and 5 dm respectively. The lateral surface area of the cuboid is a 45 m 2 b 21 m 2 c 201 m 2 d 90 m 2 Solution: Length of the cuboid, l = 15 m Breadth of the cuboid, b = 6 m Height of the cuboid, h = 5 dm = 0.5 m 1m = 10dm ? Lateral surface area of the cuboid = 2h(l + b) = 2 × 0.5 × 15 +6 = 2 × 0.5 × 21 = 21 cm 2 Hence, the correct answer is option b. Question:114 A beam 9 m long, 40 cm wide and 20 cm high is made up of iron which weighs 50 kg per cubic metre. The weight of the beam is a 27 kg b 48 kg c 36 kg d 56 kg Solution: c 36 kg Length = 9 m Breadth = 40 cm = 0.4 m Height = 20 cm = 0.2 m ? Weight of the beam = volume of the beam ×weight of iron per cubic metre = 9 ×0. 4 ×0. 2 ×50 = 36 kg Question:115 The length of the longest rod that can be placed in a room of dimensions (10 m × 10 m × 5 m) is a 15 m b 16 m c 10v 5 m d 12 m Solution: a 15 m Length of longest rod = diagonal of the room = diagonal of a cuboid = v l 2 +b 2 +h 2 = v 100 +100 +25 m = v 225 m = 15 m Question:116 What is the maximum length of a pencil that can be placed in a rectangular box of dimensions (8 cm × 6 cm × 5 cm)? a 8 cm b 9.5 cm c 19 cm d 11.2 cm ( ) Solution: d 11.2 cm Maximum length of the pencil = diagonal of the box = v l 2 +b 2 +h 2 = v 8 2 +6 2 +5 2 cm = v 64 +36 +25 cm = v 125 cm = 11. 2 cm Question:117 The number of planks of dimensions (4 m × 5 m × 2 m) that can be stored in a pit which is 40 m long, 12 m wide and 16 m deep, is a 190 b 192 c 184 d 180 Solution: b 192 Number of planks = volume of the pit volume of 1 plank = 40×12×16 4×5×2 = 7680 40 = 192 Question:118 How many planks of dimensions (5 m × 25 cm × 10 cm) can be stored in a pit which is 20 m long, 6 m wide and 50 cm deep? a 480 b 450 c 320 d 360 Solution: a 480 Length of the pit = 20 m Breadth of the pit = 6 m Height of the pit = 50 cm = 0.5 m Length of the plank = 5m Breadth of the plank = 25 cm = 0.25 m Height of the plank = 10 cm = 0.1 m ? Number of planks = volume of the pit volume of 1 plank = 20×6×0.5 5×0.25×0.1 = 60×1000 125 = 480 Question:119 How many bricks will be required to construct a wall 8 m long, 6 m high and 22.5 cm thick if each brick measures (25 cm × 11.25 cm × 6 cm)? a 4800 b 5600 c 6400 d 5200 Solution: c 6400 Length of the wall = 8 m = 800 cm Breadth of the wall = 6 m = 600 cm Height of the wall = 22.5 cm Length of the brick = 25 cm Breadth of the brick = 11.25 cm Height of the brick = 6 cm ? Number of bricks required = volume of the wall volume of 1 brick = 800×600×22.5 25×11.25×6 = 10800000 1687.5 = 6400 Question:120 How many persons can be accommodated in a dining hall of dimensions (20 m × 15 m × 4.5 m), assuming that each person requires 5 m 3 of air? a 250 b 270 c 320 d 300 Solution: b 270 Number of persons = volume of the hall volume of air required by 1 person = 20×15×4.5 5 = 20 ×3 ×4. 5 = 270 ? 270 persons can be accommodated. Question:121 A river 1.5 m deep and 30 m wide is flowing at the rate of 3 km per hour. The volume of water that runs into the sea per minute is a 2000 m 3 b 2250 m 3 c 2500 m 3 d 2750 m 3 Solution: b 2250 m 3 Length of the river = 1.5 m Breadth of the river = 30 m Depth of the river = 3 km = 3000 m Now, volume of water that runs into the sea = 1. 5 ×30 ×3000 m 3 = 135000 m 3 ? Volume of water that runs into the sea per minute = 135000 60 = 2250 m 3 Question:122 The lateral surface area of a cube is 256 m 2 . The volume of the cube is a 64 m 3 b 216 m 3 c 256 m 3 d 512 m 3 Solution: d 512 m 3 Suppose that a m be the edge of the cube. We have: 4a 2 = 256 ? a 2 = 256 4 = 64 ? a = 8 m ? Volume of the cube = a 3 m 3 = 8 3 m 3 = 512 m 3 Question:123 The total surface area of a cube is 96 cm 2 . The volume of the cube is a 8 cm 3 b 27 cm 3 c 64 cm 3 d 512 cm 3 Solution: c 64 cm 3 Let a cm be the edge of the cube. We have: 6a 2 = 96 ? a 2 = 16 ? a = 4 cm ? Volume of the cube = a 3 cm 3 = 4 3 cm 3 = 64 cm 3 Question:124 The volume of a cube is 512 cm 3 . Its total surface area is a 256 cm 2 b 384 cm 2 c 512 cm 2 d 64 cm 2 Solution: b 384 cm 2 Suppose that a cm is the edge of the cube. We have: a 3 = 512 ? a = 3 v 512 = 8 cm ? Total surface area of cube = 6a 2 cm 2 = 6 ×8 ×8 cm 2 = 384 cm 2 Question:125 The length of the longest rod that can fit in a cubical vessel of side 10 cm, is a 10 cm b 20 cm c 10v 2 cm d 10v 3 cm Solution: d 10v 3 cm Length of the longest rod = body diagonal of the vessel = v 3a = v 3 ×10 = 10v 3 cm Question:126 If the length of diagonal of a cube is 8v 3 cm, then its surface area is a 192 cm 2 b 384 cm 2 c 512 cm 2 d 768 cm 2 Solution: b 384 cm 2 We have: v 3a = 8v 3 ? a = 8 cm ? Surface area of the cube = 6a 2 = 6 ×8 ×8 = 384 cm 2 Question:127 If each edge of a cube is increased by 50%, then the percentage increase in its surface area is 10 cm Page 4 Question:111 The length, breadth and height of a cuboid are 15 cm, 12 cm and 4.5 cm respectively. Its volume is a 243 cm 3 b 405 cm 3 c 810 cm 3 d 603 cm 3 Solution: c 810 cm 3 Volume of the cuboid = l ×b ×h = 15 ×12 ×4. 5 cm 3 = 810 cm 3 Question:112 A cuboid is 12 cm long, 9 cm broad and 8 cm high. Its total surface area is a 864 cm 2 b 552 cm 2 c 432 cm 2 d 276 cm 2 Solution: b 552 cm 2 Total surface area of the cuboid = 2(lb +bh +lh) cm 2 = 2 12 ×9 +8 ×9 +12 ×8 cm 2 = 2(108 +72 +96) cm 2 Question:113 The length, breadth and height of a cuboid are 15 m, 6 m and 5 dm respectively. The lateral surface area of the cuboid is a 45 m 2 b 21 m 2 c 201 m 2 d 90 m 2 Solution: Length of the cuboid, l = 15 m Breadth of the cuboid, b = 6 m Height of the cuboid, h = 5 dm = 0.5 m 1m = 10dm ? Lateral surface area of the cuboid = 2h(l + b) = 2 × 0.5 × 15 +6 = 2 × 0.5 × 21 = 21 cm 2 Hence, the correct answer is option b. Question:114 A beam 9 m long, 40 cm wide and 20 cm high is made up of iron which weighs 50 kg per cubic metre. The weight of the beam is a 27 kg b 48 kg c 36 kg d 56 kg Solution: c 36 kg Length = 9 m Breadth = 40 cm = 0.4 m Height = 20 cm = 0.2 m ? Weight of the beam = volume of the beam ×weight of iron per cubic metre = 9 ×0. 4 ×0. 2 ×50 = 36 kg Question:115 The length of the longest rod that can be placed in a room of dimensions (10 m × 10 m × 5 m) is a 15 m b 16 m c 10v 5 m d 12 m Solution: a 15 m Length of longest rod = diagonal of the room = diagonal of a cuboid = v l 2 +b 2 +h 2 = v 100 +100 +25 m = v 225 m = 15 m Question:116 What is the maximum length of a pencil that can be placed in a rectangular box of dimensions (8 cm × 6 cm × 5 cm)? a 8 cm b 9.5 cm c 19 cm d 11.2 cm ( ) Solution: d 11.2 cm Maximum length of the pencil = diagonal of the box = v l 2 +b 2 +h 2 = v 8 2 +6 2 +5 2 cm = v 64 +36 +25 cm = v 125 cm = 11. 2 cm Question:117 The number of planks of dimensions (4 m × 5 m × 2 m) that can be stored in a pit which is 40 m long, 12 m wide and 16 m deep, is a 190 b 192 c 184 d 180 Solution: b 192 Number of planks = volume of the pit volume of 1 plank = 40×12×16 4×5×2 = 7680 40 = 192 Question:118 How many planks of dimensions (5 m × 25 cm × 10 cm) can be stored in a pit which is 20 m long, 6 m wide and 50 cm deep? a 480 b 450 c 320 d 360 Solution: a 480 Length of the pit = 20 m Breadth of the pit = 6 m Height of the pit = 50 cm = 0.5 m Length of the plank = 5m Breadth of the plank = 25 cm = 0.25 m Height of the plank = 10 cm = 0.1 m ? Number of planks = volume of the pit volume of 1 plank = 20×6×0.5 5×0.25×0.1 = 60×1000 125 = 480 Question:119 How many bricks will be required to construct a wall 8 m long, 6 m high and 22.5 cm thick if each brick measures (25 cm × 11.25 cm × 6 cm)? a 4800 b 5600 c 6400 d 5200 Solution: c 6400 Length of the wall = 8 m = 800 cm Breadth of the wall = 6 m = 600 cm Height of the wall = 22.5 cm Length of the brick = 25 cm Breadth of the brick = 11.25 cm Height of the brick = 6 cm ? Number of bricks required = volume of the wall volume of 1 brick = 800×600×22.5 25×11.25×6 = 10800000 1687.5 = 6400 Question:120 How many persons can be accommodated in a dining hall of dimensions (20 m × 15 m × 4.5 m), assuming that each person requires 5 m 3 of air? a 250 b 270 c 320 d 300 Solution: b 270 Number of persons = volume of the hall volume of air required by 1 person = 20×15×4.5 5 = 20 ×3 ×4. 5 = 270 ? 270 persons can be accommodated. Question:121 A river 1.5 m deep and 30 m wide is flowing at the rate of 3 km per hour. The volume of water that runs into the sea per minute is a 2000 m 3 b 2250 m 3 c 2500 m 3 d 2750 m 3 Solution: b 2250 m 3 Length of the river = 1.5 m Breadth of the river = 30 m Depth of the river = 3 km = 3000 m Now, volume of water that runs into the sea = 1. 5 ×30 ×3000 m 3 = 135000 m 3 ? Volume of water that runs into the sea per minute = 135000 60 = 2250 m 3 Question:122 The lateral surface area of a cube is 256 m 2 . The volume of the cube is a 64 m 3 b 216 m 3 c 256 m 3 d 512 m 3 Solution: d 512 m 3 Suppose that a m be the edge of the cube. We have: 4a 2 = 256 ? a 2 = 256 4 = 64 ? a = 8 m ? Volume of the cube = a 3 m 3 = 8 3 m 3 = 512 m 3 Question:123 The total surface area of a cube is 96 cm 2 . The volume of the cube is a 8 cm 3 b 27 cm 3 c 64 cm 3 d 512 cm 3 Solution: c 64 cm 3 Let a cm be the edge of the cube. We have: 6a 2 = 96 ? a 2 = 16 ? a = 4 cm ? Volume of the cube = a 3 cm 3 = 4 3 cm 3 = 64 cm 3 Question:124 The volume of a cube is 512 cm 3 . Its total surface area is a 256 cm 2 b 384 cm 2 c 512 cm 2 d 64 cm 2 Solution: b 384 cm 2 Suppose that a cm is the edge of the cube. We have: a 3 = 512 ? a = 3 v 512 = 8 cm ? Total surface area of cube = 6a 2 cm 2 = 6 ×8 ×8 cm 2 = 384 cm 2 Question:125 The length of the longest rod that can fit in a cubical vessel of side 10 cm, is a 10 cm b 20 cm c 10v 2 cm d 10v 3 cm Solution: d 10v 3 cm Length of the longest rod = body diagonal of the vessel = v 3a = v 3 ×10 = 10v 3 cm Question:126 If the length of diagonal of a cube is 8v 3 cm, then its surface area is a 192 cm 2 b 384 cm 2 c 512 cm 2 d 768 cm 2 Solution: b 384 cm 2 We have: v 3a = 8v 3 ? a = 8 cm ? Surface area of the cube = 6a 2 = 6 ×8 ×8 = 384 cm 2 Question:127 If each edge of a cube is increased by 50%, then the percentage increase in its surface area is 10 cm a 50% b 75% c 100% d 12% Solution: Let a be the edge of the cube. Then the surface area is 6a 2 = S say Now, increased edge = a + 50 100 a = 150 100 a = 3 2 a Then, new surface area = 6 3 2 a 2 = 6 × 9 4 a 2 = 9 4 SIncrease in surface area = 9 4 S - S = 5 4 S ? Percentage increase in surface area = 5 4 S S = 5 4 ×100 % = 125 % Question:128 Three cubes of metal with edges 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. The lateral surface area of the new cube formed is a 72 cm 2 b 144 cm 2 c 128 cm 2 d 256 cm 2 Solution: b 144 cm 2 Volume of the new cube formed = total volume of the three cubes Suppose that a cm is the edge of the new cube, then a 3 = 3 3 +4 3 +5 3 = 27 +64 +125 = 216 = 6 cm ? Lateral surface area of the new cube = 4a 2 = 4 ×6 ×6 = 144 cm 2 Question:129 In a shower, 5 cm of rain falls. What is the volume of water that falls on 2 hectares of ground? a 500 m 3 b 750 m 3 c 800 m 3 d 1000 m 3 Solution: d 1000 m 3 Area of the land = 2 sq hec = 2000 sq mAmount of rainfall = 5 cm = 0. 05 m ? Volume of the water = area of the land ×amount of rainfall = 2000 ×0. 05 Question:130 Two cubes have their volumes in the ratio 1 : 27. The ratio of their surface areas is a 1 : 3 b 1 : 8 c 1 : 9 d 1 : 18 Solution: c 1 : 9 Suppose that the edges of the cubes are a and b. We have: a 3 b 3 = 1 27 ? a b 3 = 1 27 ? a b = 1 3 ? Ratio of the surface areas = 6a 2 6b 2 = a b 2 = 1 3 2 = 1 9 Question:131 If each side of a cube is doubled, then its volume a is doubled b becomes 4 times c becomes 6 times d becomes 8 times Solution: d becomes 8 times Suppose that the side of the cube is a. When it is doubled, it becomes 2a. New volume of the cube = (2a) 3 = 8a 3 Hence, the volume becomes 8 times the original volume. Question:132 The diameter of the base of a cylinder is 6 cm and its height is 14 cm. The volume of the cylinder is a 198 cm 3 b 396 cm 3 c 495 cm 3 d 297 cm 3 Solution: b 396 cm 3 Volume of the cylinder = pr 2 h = 22 7 ×3 2 ×14 = 22 ×9 ×2 = 396 cm 3 ( ) ( ) ( ) ( ) ( ) ( ) Page 5 Question:111 The length, breadth and height of a cuboid are 15 cm, 12 cm and 4.5 cm respectively. Its volume is a 243 cm 3 b 405 cm 3 c 810 cm 3 d 603 cm 3 Solution: c 810 cm 3 Volume of the cuboid = l ×b ×h = 15 ×12 ×4. 5 cm 3 = 810 cm 3 Question:112 A cuboid is 12 cm long, 9 cm broad and 8 cm high. Its total surface area is a 864 cm 2 b 552 cm 2 c 432 cm 2 d 276 cm 2 Solution: b 552 cm 2 Total surface area of the cuboid = 2(lb +bh +lh) cm 2 = 2 12 ×9 +8 ×9 +12 ×8 cm 2 = 2(108 +72 +96) cm 2 Question:113 The length, breadth and height of a cuboid are 15 m, 6 m and 5 dm respectively. The lateral surface area of the cuboid is a 45 m 2 b 21 m 2 c 201 m 2 d 90 m 2 Solution: Length of the cuboid, l = 15 m Breadth of the cuboid, b = 6 m Height of the cuboid, h = 5 dm = 0.5 m 1m = 10dm ? Lateral surface area of the cuboid = 2h(l + b) = 2 × 0.5 × 15 +6 = 2 × 0.5 × 21 = 21 cm 2 Hence, the correct answer is option b. Question:114 A beam 9 m long, 40 cm wide and 20 cm high is made up of iron which weighs 50 kg per cubic metre. The weight of the beam is a 27 kg b 48 kg c 36 kg d 56 kg Solution: c 36 kg Length = 9 m Breadth = 40 cm = 0.4 m Height = 20 cm = 0.2 m ? Weight of the beam = volume of the beam ×weight of iron per cubic metre = 9 ×0. 4 ×0. 2 ×50 = 36 kg Question:115 The length of the longest rod that can be placed in a room of dimensions (10 m × 10 m × 5 m) is a 15 m b 16 m c 10v 5 m d 12 m Solution: a 15 m Length of longest rod = diagonal of the room = diagonal of a cuboid = v l 2 +b 2 +h 2 = v 100 +100 +25 m = v 225 m = 15 m Question:116 What is the maximum length of a pencil that can be placed in a rectangular box of dimensions (8 cm × 6 cm × 5 cm)? a 8 cm b 9.5 cm c 19 cm d 11.2 cm ( ) Solution: d 11.2 cm Maximum length of the pencil = diagonal of the box = v l 2 +b 2 +h 2 = v 8 2 +6 2 +5 2 cm = v 64 +36 +25 cm = v 125 cm = 11. 2 cm Question:117 The number of planks of dimensions (4 m × 5 m × 2 m) that can be stored in a pit which is 40 m long, 12 m wide and 16 m deep, is a 190 b 192 c 184 d 180 Solution: b 192 Number of planks = volume of the pit volume of 1 plank = 40×12×16 4×5×2 = 7680 40 = 192 Question:118 How many planks of dimensions (5 m × 25 cm × 10 cm) can be stored in a pit which is 20 m long, 6 m wide and 50 cm deep? a 480 b 450 c 320 d 360 Solution: a 480 Length of the pit = 20 m Breadth of the pit = 6 m Height of the pit = 50 cm = 0.5 m Length of the plank = 5m Breadth of the plank = 25 cm = 0.25 m Height of the plank = 10 cm = 0.1 m ? Number of planks = volume of the pit volume of 1 plank = 20×6×0.5 5×0.25×0.1 = 60×1000 125 = 480 Question:119 How many bricks will be required to construct a wall 8 m long, 6 m high and 22.5 cm thick if each brick measures (25 cm × 11.25 cm × 6 cm)? a 4800 b 5600 c 6400 d 5200 Solution: c 6400 Length of the wall = 8 m = 800 cm Breadth of the wall = 6 m = 600 cm Height of the wall = 22.5 cm Length of the brick = 25 cm Breadth of the brick = 11.25 cm Height of the brick = 6 cm ? Number of bricks required = volume of the wall volume of 1 brick = 800×600×22.5 25×11.25×6 = 10800000 1687.5 = 6400 Question:120 How many persons can be accommodated in a dining hall of dimensions (20 m × 15 m × 4.5 m), assuming that each person requires 5 m 3 of air? a 250 b 270 c 320 d 300 Solution: b 270 Number of persons = volume of the hall volume of air required by 1 person = 20×15×4.5 5 = 20 ×3 ×4. 5 = 270 ? 270 persons can be accommodated. Question:121 A river 1.5 m deep and 30 m wide is flowing at the rate of 3 km per hour. The volume of water that runs into the sea per minute is a 2000 m 3 b 2250 m 3 c 2500 m 3 d 2750 m 3 Solution: b 2250 m 3 Length of the river = 1.5 m Breadth of the river = 30 m Depth of the river = 3 km = 3000 m Now, volume of water that runs into the sea = 1. 5 ×30 ×3000 m 3 = 135000 m 3 ? Volume of water that runs into the sea per minute = 135000 60 = 2250 m 3 Question:122 The lateral surface area of a cube is 256 m 2 . The volume of the cube is a 64 m 3 b 216 m 3 c 256 m 3 d 512 m 3 Solution: d 512 m 3 Suppose that a m be the edge of the cube. We have: 4a 2 = 256 ? a 2 = 256 4 = 64 ? a = 8 m ? Volume of the cube = a 3 m 3 = 8 3 m 3 = 512 m 3 Question:123 The total surface area of a cube is 96 cm 2 . The volume of the cube is a 8 cm 3 b 27 cm 3 c 64 cm 3 d 512 cm 3 Solution: c 64 cm 3 Let a cm be the edge of the cube. We have: 6a 2 = 96 ? a 2 = 16 ? a = 4 cm ? Volume of the cube = a 3 cm 3 = 4 3 cm 3 = 64 cm 3 Question:124 The volume of a cube is 512 cm 3 . Its total surface area is a 256 cm 2 b 384 cm 2 c 512 cm 2 d 64 cm 2 Solution: b 384 cm 2 Suppose that a cm is the edge of the cube. We have: a 3 = 512 ? a = 3 v 512 = 8 cm ? Total surface area of cube = 6a 2 cm 2 = 6 ×8 ×8 cm 2 = 384 cm 2 Question:125 The length of the longest rod that can fit in a cubical vessel of side 10 cm, is a 10 cm b 20 cm c 10v 2 cm d 10v 3 cm Solution: d 10v 3 cm Length of the longest rod = body diagonal of the vessel = v 3a = v 3 ×10 = 10v 3 cm Question:126 If the length of diagonal of a cube is 8v 3 cm, then its surface area is a 192 cm 2 b 384 cm 2 c 512 cm 2 d 768 cm 2 Solution: b 384 cm 2 We have: v 3a = 8v 3 ? a = 8 cm ? Surface area of the cube = 6a 2 = 6 ×8 ×8 = 384 cm 2 Question:127 If each edge of a cube is increased by 50%, then the percentage increase in its surface area is 10 cm a 50% b 75% c 100% d 12% Solution: Let a be the edge of the cube. Then the surface area is 6a 2 = S say Now, increased edge = a + 50 100 a = 150 100 a = 3 2 a Then, new surface area = 6 3 2 a 2 = 6 × 9 4 a 2 = 9 4 SIncrease in surface area = 9 4 S - S = 5 4 S ? Percentage increase in surface area = 5 4 S S = 5 4 ×100 % = 125 % Question:128 Three cubes of metal with edges 3 cm, 4 cm and 5 cm respectively are melted to form a single cube. The lateral surface area of the new cube formed is a 72 cm 2 b 144 cm 2 c 128 cm 2 d 256 cm 2 Solution: b 144 cm 2 Volume of the new cube formed = total volume of the three cubes Suppose that a cm is the edge of the new cube, then a 3 = 3 3 +4 3 +5 3 = 27 +64 +125 = 216 = 6 cm ? Lateral surface area of the new cube = 4a 2 = 4 ×6 ×6 = 144 cm 2 Question:129 In a shower, 5 cm of rain falls. What is the volume of water that falls on 2 hectares of ground? a 500 m 3 b 750 m 3 c 800 m 3 d 1000 m 3 Solution: d 1000 m 3 Area of the land = 2 sq hec = 2000 sq mAmount of rainfall = 5 cm = 0. 05 m ? Volume of the water = area of the land ×amount of rainfall = 2000 ×0. 05 Question:130 Two cubes have their volumes in the ratio 1 : 27. The ratio of their surface areas is a 1 : 3 b 1 : 8 c 1 : 9 d 1 : 18 Solution: c 1 : 9 Suppose that the edges of the cubes are a and b. We have: a 3 b 3 = 1 27 ? a b 3 = 1 27 ? a b = 1 3 ? Ratio of the surface areas = 6a 2 6b 2 = a b 2 = 1 3 2 = 1 9 Question:131 If each side of a cube is doubled, then its volume a is doubled b becomes 4 times c becomes 6 times d becomes 8 times Solution: d becomes 8 times Suppose that the side of the cube is a. When it is doubled, it becomes 2a. New volume of the cube = (2a) 3 = 8a 3 Hence, the volume becomes 8 times the original volume. Question:132 The diameter of the base of a cylinder is 6 cm and its height is 14 cm. The volume of the cylinder is a 198 cm 3 b 396 cm 3 c 495 cm 3 d 297 cm 3 Solution: b 396 cm 3 Volume of the cylinder = pr 2 h = 22 7 ×3 2 ×14 = 22 ×9 ×2 = 396 cm 3 ( ) ( ) ( ) ( ) ( ) ( ) Question:133 If the diameter of a cylinder is 28 cm and its height is 20 cm, then its curved surface area is a 880 cm 2 b 1760 cm 2 c 3520 cm 2 d 2640 cm 2 Solution: b 1760 cm 2 Curved surface area of the cylinder = 2 prh = 2 × 22 7 ×14 ×20 = 44 ×40 = 1760 Question:134 If the curved surface area of a cylinder is 1760 cm 2 and its base radius is 14 cm, then its height is a 10 cm b 15 cm c 20 cm d 40 cm Solution: c 20 cm Curved surface area = 1760 cm 2 Suppose that h cm is the height of the cylinder. Then we have: 2 prh = 1760 ? 2 × 22 7 ×14 ×h = 1760 ? h = 1760×7 44×14 = 20 cm Question:135 The height of a cylinder is 14 cm and its curved surface area is 264 cm 2 . The volume of the cylinder is a 308 cm 3 b 396 cm 3 c 1232 cm 3 d 1848 cm 3 Solution: b 396 cm 3 Curved surface area = 264 cm 2 . Let r cm be the radius of the cylinder. Then we have: 2 prh = 264 ? 2 × 22 7 ×r×14 = 264 ? r = 264×7 44×14 = 3 cm ? Volume of the cylinder = 22 7 ×3 2 ×14 = 22 ×9 ×2 = 396 cm 3 Question:136 The curved surface area of a cylindrical pillar is 264 m 2 and its volume is 924 m 3 . The height of the pillar is a 4 m b 5 m c 6 m d 7 m Solution: c 6 m Curved surface area = 264 m 2 Volume = 924 m 3 Let r m be the radius and h m be the height of the cylinder. Then we have: 2 prh = 264 and pr 2 h = 924 ? rh = 264 2 p ? h = 264 2r× p Now, pr 2 h = p ×r 2 × 264 2r× p = 924 ? r = 924×2 264 ? r = 7 m ? h = 264×7 2×7×22 = 6 m Question:137 The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their curved surface area is a 2 : 5 b 8 : 7 c 10 : 9 d 16 : 9 Solution: c 10 : 9 Suppose that the radii of the cylinders are 2r and 3r and their respective heights are 5h and 3h. Then, ratio of the curved surface areas = 2 p (2r)(5h) 2 p (3r)(3h) =10 : 9 Question:138 The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is a 27 : 20 b 20 : 27 c 4 : 9 d 9 : 4 Solution: b 20 : 27 Suppose that the radii of the cylinders are 2r and 3r and their respective heights are 5h and 3h..Read More

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