IUC AcademyHome561. If the radius and height of a right circular cylinder are 21 cm and 35 cm respectively, then the total surface area of the cylinder is
- A. 7092 sq cm
- B. 7192 sq cm
- C. 7292 sq cm
- D. 7392 sq cm
Answer: 7392 sq cm
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562. Find the cost of a cylinder of radius 14 m and height 3.5 m when the cost of its metal is ₹ 50 per cubic metre.
- A. ₹ 100208
- B. ₹ 107800
- C. ₹ 10800
- D. ₹ 109800
Answer: ₹ 107800
563. A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What is the volume of the earth dug out?
- A. 32 m3
- B. 36 m3
- C. 40 m3
- D. 44 m3
Answer: 44 m3
564. A cube of edge 20 cm is completely immersed in a rectangular vessel containing water. If the dimen-sions of the base of the vessel are 20 cm by 40 cm, the rise in water level will be
- A. 2 cm
- B. 8 cm
- C. 10 cm
- D. 14 cm
Answer: 10 cm
565. If each edge of a cube is increased by 25%, then the percentage increase in its surface area is :
- A. 25%
- B. 48.75%
- C. 50%
- D. 56.25%
Answer: 56.25%
566. By what percent the volume of a cube increases if the length of each edge was increased by 50%?
- A. 50%
- B. 125%
- C. 237.5%
- D. 273.5%
Answer: 237.5%
567. If each edge of a cube is doubled, then its volume:
- A. is doubled
- B. becomes 4 times
- C. becomes 6 times
- D. becomes 8 times
Answer: becomes 8 times
Explanation: Let original edge = a. Then, volume = a3. New edge = 2a. So, new volume = (2a) 3 = 8a3. ∴ Volume becomes 8 times.
Explanation: Let original edge = a. Then, volume = a3. New edge = 2a. So, new volume = (2a) 3 = 8a3. ∴ Volume becomes 8 times.
568. Two cubes have volumes in the ratio 1 : 27. Then the ratio of the area of the face of one of the cubes to that of the other is
- A. 1 : 3 / 1: 3
- B. 1 : 6 / 1: 6
- C. 1 : 9 / 1: 9
- D. 1 : 12 / 1: 12
Answer: 1 : 9 / 1: 9
569. The volumes of two cubes are in the ratio 8 : 27. The ratio of their surface areas is
- A. 2 : 3 / 2: 3
- B. 4 : 9 / 4: 9
- C. 12 : 9 / 12: 9
- D. None of these
Answer: 4 : 9 / 4: 9
570. If the volumes of two cubes are in the ratio 27 : 1, the ratio of their edges is
- A. 1 : 3 / 1: 3
- B. 1 : 27 / 1: 27
- C. 3 : 1 / 3: 1
- D. 27 : 1 / 27: 1
Answer: 3 : 1 / 3: 1
571. Three cubes with sides in the ratio 3 : 4 : 5 are melted to form a single cube whose diagonal is 12 3 cm. The sides of the cubes are
- A. 3 cm, 4 cm, 5 cm
- B. 6 cm, 8 cm, 10 cm
- C. 9 cm, 12 cm, 15 cm
- D. None of these
Answer: 6 cm, 8 cm, 10 cm
572. If three equal cubes are placed adjacently in a row, then the ratio of the total surface area of the new cuboid to the sum of the surface areas of the three cubes will be
- A. 1 : 3 / 1: 3
- B. 2 : 3 / 2: 3
- C. 5 : 9 / 5: 9
- D. 7 : 9 / 7: 9
Answer: 7 : 9 / 7: 9
Explanation: Let the length of each edge of each cube be a. Then, the cuboid formed by placing 3 cubes adjacently has the dimensions 3a, a and a. Surface area of the cuboid = 2 [3a × a + a × a + 3a × a] = 2 (3a2 + a2 + 3a2) = 14a2. Sum of surface areas of 3 cubes = (3 × 6a2) = 18a2. ∴ Required ratio = 14a2: 18a2 = 7 : 9.
Explanation: Let the length of each edge of each cube be a. Then, the cuboid formed by placing 3 cubes adjacently has the dimensions 3a, a and a. Surface area of the cuboid = 2 [3a × a + a × a + 3a × a] = 2 (3a2 + a2 + 3a2) = 14a2. Sum of surface areas of 3 cubes = (3 × 6a2) = 18a2. ∴ Required ratio = 14a2: 18a2 = 7 : 9.
573. Five equal cubes, each of side 5 cm, are placed adjacent to each other. The volume of the new solid formed will be
- A. 125 cm3
- B. 625 cm3
- C. 15525 cm3
- D. None of these
Answer: 625 cm3
Explanation: The new solid formed is a cuboid of length 25 cm, breadth 5 cm and height 5 cm. ∴ Volume = (25 × 5 × 5) cm3 = 625 cm3.
Explanation: The new solid formed is a cuboid of length 25 cm, breadth 5 cm and height 5 cm. ∴ Volume = (25 × 5 × 5) cm3 = 625 cm3.
574. A larger cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. The ratio of the total surface areas of the smaller cubes and the larger cube is
- A. 2 : 1 / 2: 1
- B. 3 : 2 / 3: 2
- C. 25 : 18 / 25: 18
- D. 27 : 20 / 27: 20
Answer: 25 : 18 / 25: 18
575. If three cubes of copper, each with an edge of 6 cm 8 cm and 10 cm respectively are melted to form a single cube, then the diagonal of the new cube will be
- A. 18 cm
- B. 19 cm
- C. 19.5 cm
- D. 20.8 cm
Answer: 20.8 cm
Explanation: Volume of the new cube = (63 + 83 + 103) cm3 = 1728 cm3. Let the edge of the new cube be a cm. ∴ a3 = 1728 ⇒ a = 12. Hence, length of diagonal = 3 12 3 cm a = = (12 × 1.732) cm = 20.784 cm ≈ 20.8 cm.
Explanation: Volume of the new cube = (63 + 83 + 103) cm3 = 1728 cm3. Let the edge of the new cube be a cm. ∴ a3 = 1728 ⇒ a = 12. Hence, length of diagonal = 3 12 3 cm a = = (12 × 1.732) cm = 20.784 cm ≈ 20.8 cm.
576. There is a cube of volume 216 cm3. It is to be moulded into a cuboid having one edge equal to 6 cm. The number of ways that it can be done so that the edges have different integral values is
- A. 1
- B. 2
- C. 3
- D. 4
Answer: 4
Explanation: Let the other two dimensions of the cuboid be a and b cm respectively. Then, 6ab = 216 or ab = 36. The possible values of (a, b) are (1, 36), (2, 18), (3, 12) and (4, 9).
Explanation: Let the other two dimensions of the cuboid be a and b cm respectively. Then, 6ab = 216 or ab = 36. The possible values of (a, b) are (1, 36), (2, 18), (3, 12) and (4, 9).
577. A cube of white chalk is painted red, and then cut parallel to the sides to form two rectangular solids of equal volumes. What percent of the surface area of each of the new solids is not painted red?
- A. 15%
- B. 16⅔%
- C. 20%
- D. 25%
Answer: 25%
578. An iron cube of side 10 cm is hammered into a rectangular sheet of thickness 0.5 cm. If the sides of the sheet are in the ratio 1 : 5, the sides are
- A. 10 cm, 50 cm
- B. 20 cm, 100 cm
- C. 40 cm, 200 cm
- D. None of these
Answer: 20 cm, 100 cm
579. The size of a wooden block is 5 × 10 × 20 cm. How many such blocks will be required to construct a solid wooden cube of minimum size?
- A. 6
- B. 8
- C. 12
- D. 16
Answer: 8
580. A cuboidal block of 6 cm × 9 cm × 12 cm is cut up into an exact number of equal cubes. The least possible number of cubes will be
- A. 6
- B. 9
- C. 24
- D. 30
Answer: 24
581. The volume of a cuboid is twice that of a cube. If the dimensions of the cuboid are 9 cm, 8 cm and 6 cm, the total surface area of the cube is
- A. 72 cm2
- B. 108 cm2
- C. 216 cm2
- D. 432 cm2
Answer: 216 cm2
582. How many small cubes, each of 96 cm surface area, can be formed from the material obtained by melting a larger cube of 384 cm surface area?
- A. 5
- B. 8
- C. 800
- D. 8000
Answer: 8
583. Shobhraj takes a cube of 1 m edge-length and me-ticulously cuts smaller cubes, each of edge-length 1 mm from the parent cube. He joins these small cubes end-to-end. Thus, the total length of this ‘cube-robe’ will be
- A. 1 km
- B. 10 km
- C. 100 km
- D. 1000 km
Answer: 1000 km
584. How many cubes of 3 cm edge can be cut out of a cube of 18 cm edge?
- A. 36
- B. 216
- C. 218
- D. 432
Answer: 216
585. A rectangular box measures internally 1.6 m long, 1 m broad and 60 cm deep. The number of cubical blocks each of edge 20 cm that can be packed inside the box is
- A. 30
- B. 53
- C. 60
- D. 120
Answer: 120
586. A rectangular block with a volume of 250 cm3 was sliced into two cubes of equal volume. How much greater (in sq. cm) is the combined surface area of the two cubes then the original surface area of the rectangular block?
- A. 48.64
- B. 50
- C. 56.25
- D. 84.67
Answer: 50
587. A 4 cm cube is cut into 1 cm cubes. The total surface area of all the small cubes is
- A. 24 cm2
- B. 96 cm2
- C. 384 cm2
- D. None of these
Answer: 384 cm2
588. How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?
- A. 10
- B. 100
- C. 1000
- D. 10000
Answer: 1000
589. A cube of length 1 cm is taken out from a cube of length 8 cm. What is the weight of the remaining portion?
- A. 7 8 of the weight of the original cube
- B. 8 9 of the weight of the original cube
- C. 63 64 of the weight of the original cube
- D. 511 512 of the weight of the original cube
Answer: 511 512 of the weight of the original cube
Explanation: Volume of the bigger cube = (83) cm3 = 512 cm3. Volume of the cut-out cube = (13) cm3 = 1 cm3. Volume of the remaining portion = (512 – 1) cm3 = 511 cm3. Weight of the remaining portion Weight of the original cube = 511. 512
Explanation: Volume of the bigger cube = (83) cm3 = 512 cm3. Volume of the cut-out cube = (13) cm3 = 1 cm3. Volume of the remaining portion = (512 – 1) cm3 = 511 cm3. Weight of the remaining portion Weight of the original cube = 511. 512
590. A solid cube just gets completely immersed in water when a 0.2 kg mass is placed on it. If the mass is removed, the cube is 2 cm above the water level. What is the length of each side of the cube?
- A. 6 cm
- B. 8 cm
- C. 10 cm
- D. 12 cm
Answer: 10 cm
Explanation: Let the length of each side of the cube be a cm. Then, volume of the part of cube outside water = volume of the mass placed on it ⇒ 2a2 = 0.2 × 1000 = 200 ⇒ a2 = 100 ⇒ a = 10.
Explanation: Let the length of each side of the cube be a cm. Then, volume of the part of cube outside water = volume of the mass placed on it ⇒ 2a2 = 0.2 × 1000 = 200 ⇒ a2 = 100 ⇒ a = 10.
591. Except for one face of a given cube, identical cubes are glued through their faces to all the other faces of the given cube. If each side of the given cube measures 3 cm, then what is the total surface area of the solid body thus formed?
- A. 225 cm2
- B. 234 cm2
- C. 270 cm2
- D. 279 cm2
Answer: 234 cm2
Explanation: Clearly, each of the 5 faces of the given cube are glued to a face of another cube. ∴ Total surface area of the solid 5 × 5a2 + a2 = 26a2 = (26 × 32) cm2 = 234 cm2.
Explanation: Clearly, each of the 5 faces of the given cube are glued to a face of another cube. ∴ Total surface area of the solid 5 × 5a2 + a2 = 26a2 = (26 × 32) cm2 = 234 cm2.
592. The volume of a cube is numerically equal to the sum of its edges. What is its total surface area in square units?
- A. 36
- B. 66
- C. 72
- D. 183
Answer: 72
593. If the numbers representing volume and surface area of a cube are equal, then the length of the edge of the cube in terms of the unit of measurement will be
- A. 3
- B. 4
- C. 5
- D. 6
Answer: 6
594. From a cube of side 8m, a square hole of 3m side is hollowed from end to end. What is the volume of the remaining solid?
- A. 440 m3
- B. 480 m3
- C. 508 m3
- D. 520 m3
Answer: 440 m3
Explanation: Volume of the remaining solid = Volume of the cube – Volume of the cuboid cut out fromit = [(8 × 8 × 8) – (3 × 3 × 8)] m3 = (512 – 72) m3 = 440 m3.
Explanation: Volume of the remaining solid = Volume of the cube – Volume of the cuboid cut out fromit = [(8 × 8 × 8) – (3 × 3 × 8)] m3 = (512 – 72) m3 = 440 m3.
595. V1, V2, V3 and V4 are the volumes of four cubes of side lengths x cm, 2x cm, 3x cm and 4x cm respec-tively. Some statements regarding these volumes are given below (1) V1 + V2 + 2V3 < V4 (2) V1 + 4V2 + V3 < V4 (3) 2(V1 + V3) + V2 = V4 Which of these statements are correct?
- A. 1 and 2
- B. 2 and 3
- C. 1 and 3
- D. 1, 2 and 3
Answer: 1, 2 and 3
Explanation: Clearly, we have: V1 = x3, V2 = (2x)3 = 8x3, V3 = (3x)3 = 27x3, V4 = (4x) 3 = 64x3. (1) V1 + V2 + 2V3 = x3 + 8x3 + 2 × 27x3 = 63x3 < V4. (2) V1 + 4V2 + V3 = x3 + 4 × 8x3 + 27x3 = 60x3 < V4. (3) 2(V1 + V3) + V2 = 2(x3 + 27x3) + 8x3 = 64x3 = V4.
Explanation: Clearly, we have: V1 = x3, V2 = (2x)3 = 8x3, V3 = (3x)3 = 27x3, V4 = (4x) 3 = 64x3. (1) V1 + V2 + 2V3 = x3 + 8x3 + 2 × 27x3 = 63x3 < V4. (2) V1 + 4V2 + V3 = x3 + 4 × 8x3 + 27x3 = 60x3 < V4. (3) 2(V1 + V3) + V2 = 2(x3 + 27x3) + 8x3 = 64x3 = V4.
596. If the surface area of a cube is 13254 cm2, then the length of its diagonal is
- A. 44 3 cm
- B. 45 3 cm
- C. 46 3 cm
- D. 47 3 cm
Answer: 47 3 cm
597. If the total length of diagonals of a cube is 12 cm, then what is the total length of the edges of the cube?
- A. 6 3 cm
- B. 12 cm
- C. 15 cm
- D. 12 3 cm
Answer: 15 cm
598. What is the volume of a cube (in cubic cm) whose diagonal measures 4 3 cm?
- A. 8
- B. 16
- C. 27
- D. 64
Answer: 64
Explanation: 3 4 3 4. a a = ⇒= ∴ Volume = (4 × 4 × 4) cm3 = 64 cm3.
Explanation: 3 4 3 4. a a = ⇒= ∴ Volume = (4 × 4 × 4) cm3 = 64 cm3.
599. An aluminium sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference in the surface areas of the two solids would be
- A. Nil
- B. 284 cm2
- C. 286 cm2
- D. 296 cm2
Answer: 286 cm2
Explanation: Volume of cube = Volume of sheet = (27 × 8 × 1) cm3 = 216 cm3. Edge of cube = 3 216 cm 6 cm. = Surface area of sheet= 2(lb + bh + lh) = 2 (27 × 8 + 8 × 1 + 27 × 1) cm2. = (216 + 8 + 27) cm2 = 502 cm2. Surface area of cube = 6a2 = (6 × 62) cm2 = 216 cm2. ∴ Required difference = (502 – 216) cm2 = 286 cm2.
Explanation: Volume of cube = Volume of sheet = (27 × 8 × 1) cm3 = 216 cm3. Edge of cube = 3 216 cm 6 cm. = Surface area of sheet= 2(lb + bh + lh) = 2 (27 × 8 + 8 × 1 + 27 × 1) cm2. = (216 + 8 + 27) cm2 = 502 cm2. Surface area of cube = 6a2 = (6 × 62) cm2 = 216 cm2. ∴ Required difference = (502 – 216) cm2 = 286 cm2.
600. The cost of painting the whole surface area of a cube at the rate of 13 paise per sq. cm is ₹ 343.98. Then the volume of the cube is :
- A. 8500 cm3
- B. 9000 cm3
- C. 9250 cm3
- D. 9261 cm3
Answer: 9261 cm3
601. The dimensions of a piece of iron in the shape of a cuboid are 270 cm × 100 cm × 64 cm. If it is melted and recast into a cube, then the surface area of the cube will be
- A. 14400 cm2
- B. 44200 cm2
- C. 57600 cm2
- D. 86400 cm2
Answer: 86400 cm2
Explanation: Volume of the cube = (270 × 100 × 64) cm3. Edge of the cube = 3 270 100 64 cm (3 10 4) cm 120 cm. × × =× × = ∴ Surface area = (6 × 120 × 120) cm2 = 86400 cm2.
Explanation: Volume of the cube = (270 × 100 × 64) cm3. Edge of the cube = 3 270 100 64 cm (3 10 4) cm 120 cm. × × =× × = ∴ Surface area = (6 × 120 × 120) cm2 = 86400 cm2.
602. The surface area of a cube is 150 cm2. Its volume is
- A. 64 cm3
- B. 125 cm3
- C. 150 cm3
- D. 216 cm3
Answer: 125 cm3
603. If the volume of a cube is 729 cm3, then the surface area of the cube will be
- A. 456 cm2
- B. 466 cm2
- C. 476 cm2
- D. 486 cm2
Answer: 486 cm2
604. The cost of the paint is ₹ 36.50 per kg. If 1 kg of paint covers 16 square feet, how much will it cost to paint outside of a cube having 8 feet each side?
- A. ₹ 692
- B. ₹ 768
- C. ₹ 876
- D. ₹ 972
Answer: ₹ 876
605. Total surface area of a cube whose side is 0.5 cm is
- A. 1 2 cm 4
- B. 1 2 cm8
- C. 3 2 cm 4
- D. 3 2 cm2
Answer: 3 2 cm2
606. The perimeter of one face of a cube is 20 cm. Its volume must be
- A. 125 cm3
- B. 400 cm3
- C. 1000 cm3
- D. 8000 cm3
Answer: 125 cm3
607. Each side of a cube measures 8 metres. What is the volume of the cube?
- A. 72 cu. m
- B. 144 cu. m
- C. 196 cu. m
- D. None of these
Answer: None of these
608. Rahul hired a contractor to dig a well of 10 metres length, 10 metres breadth and 10 metres depth for ₹ 40000. However, when the contractor was about to start the work, he changed his mind and asked him to get two wells dug, each with a length of 5 metres, breadth of 5 metres and depth of 5 metres. How much should Rahul pay to the contractor?
- A. ₹ 10000
- B. ₹ 20000
- C. ₹ 40000
- D. None of these
Answer: ₹ 10000
609. If a metal slab of size 1 m × 20 cm × 1 cm is melted to another slab of 1 mm thickness and 1 m width, then the length of the new slab thus formed will be
- A. 200 cm
- B. 400 cm
- C. 600 cm
- D. 1000 cm
Answer: 200 cm
610. The dimensions of a certain machine are 48″ × 30″ × 52″. If the size of the machine is increased proportionately until the sum of its dimensions equals 156″, what will be the increase in the shortest side?
- A. 4″
- B. 6″
- C. 8″
- D. 9″
Answer: 6″
611. If the areas of three adjacent faces of a rectangular block are in the ratio of 2 : 3 : 4 and its volume is 9000 cu. cm; then the length of the shortest side is
- A. 10 cm
- B. 15 cm
- C. 20 cm
- D. 30 cm
Answer: 15 cm
612. If the areas of the three adjacent faces of a cuboidal box are 120 cm2, 72 cm2 and 60 cm2 respectively, then find the volume of the box.
- A. 720 cm3
- B. 864 cm3
- C. 7200 cm3
- D. (72)2 cm3
Answer: 720 cm3
613. A rectangular water tank is open at the top. Its capacity is 24 m3. Its length and breadth are 4 m and 3 m respectively. Ignoring the thickness of the material used for building the tank, the total cost of painting the inner and outer surfaces of the tank at the rate of ₹ 10 per m2 is
- A. ₹ 400
- B. ₹ 500
- C. ₹ 600
- D. ₹ 800
Answer: ₹ 800
614. If a metallic cuboid weighs 16 kg, how much would a miniature cuboid of metal weigh, if all dimensions are reduced to one-fourth of the original?
- A. 0.25 kg
- B. 0.50 kg
- C. 0.75 kg
- D. 1 kg
Answer: 0.25 kg
615. A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is
- A. 90 cm
- B. 1 dm
- C. 1 m
- D. 1.1 m
Answer: 1 dm
616. An open wooden box has walls 3 cm thick and outer dimensions 1.46 m, 1.16 m and 8.3 dm. What does it cost to paint its inner surface at 50 paise per 100 sq. cm?
- A. ₹ 138.50
- B. ₹ 277
- C. ₹ 415. 50
- D. ₹ 554
Answer: ₹ 277
617. The dimensions of an open box are 52 cm × 40 cm × 29 cm. Its thickness is 2 cm. If 1 cu. cm of metal used in the box weighs 0.5 gm, then the weight of the box is
- A. 6.832 kg
- B. 7.576 kg
- C. 7.76 kg
- D. 8.56 kg
Answer: 6.832 kg
618. A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm and the thickness of wood is 2.5 cm. Find the volume of the wood.
- A. 81000 cu.cm
- B. 81775 cu.cm
- C. 82125 cu.cm
- D. None of these
Answer: 82125 cu.cm
Explanation: The external measures of the box are (115 + 5) cm, (75 + 5) cm and (35 + 5) cm i.e., 120 cm, 80 cm and 40 cm. Volume of the wood = External volume – Internal volume = [(120 × 80 × 40) – (115 × 75 × 35)] cm3 = (384000 – 301875) cm3 = 82125 cm3.
Explanation: The external measures of the box are (115 + 5) cm, (75 + 5) cm and (35 + 5) cm i.e., 120 cm, 80 cm and 40 cm. Volume of the wood = External volume – Internal volume = [(120 × 80 × 40) – (115 × 75 × 35)] cm3 = (384000 – 301875) cm3 = 82125 cm3.
619. A closed box made of wood of uniform thickness has length, breadth and height 12 cm, 10 cm and 8 cm respectively. If the thickness of the wood is 1 cm, the inner surface area is
- A. 264 cm2
- B. 376 cm2
- C. 456 cm2
- D. 696 cm2
Answer: 376 cm2
Explanation: Internal length = (12 – 2) cm = 10 cm, Internal breadth = (10 – 2) cm = 8 cm, Internal height = (8 – 2) cm = 6 cm. Inner surface area = 2 [10 × 8 + 8 × 6 + 10 × 6] cm2 = (2 × 188) cm2 = 376 cm2.
Explanation: Internal length = (12 – 2) cm = 10 cm, Internal breadth = (10 – 2) cm = 8 cm, Internal height = (8 – 2) cm = 6 cm. Inner surface area = 2 [10 × 8 + 8 × 6 + 10 × 6] cm2 = (2 × 188) cm2 = 376 cm2.
620. An open box is made by cutting the congruent squares from the corners of a rectangular sheet of cardboard of dimensions 20 cm × 15 cm. If the side of each square is 2 cm, the total outer surface area of the box is
- A. 148 cm2
- B. 284 cm2
- C. 316 cm2
- D. 460 cm2
Answer: 284 cm2
Explanation: Clearly, l = (20 – 4) cm = 16 cm, b = (15 – 4) cm = 11 cm, h = 2cm ∴ Outer surface area of the box = [2 (l + b) × h] + lb = [{2 (16 + 11) × 2} + 16 × 11] cm2 = (108 + 176) cm2 = 284 cm2.
Explanation: Clearly, l = (20 – 4) cm = 16 cm, b = (15 – 4) cm = 11 cm, h = 2cm ∴ Outer surface area of the box = [2 (l + b) × h] + lb = [{2 (16 + 11) × 2} + 16 × 11] cm2 = (108 + 176) cm2 = 284 cm2.
621. An open box is made from a 18 cm × 24 cm rectangular cardboard by cutting a 5 cm square from each corner and folding up the sides. Find the box's volume in cu. cm.
- A. 216
- B. 432
- C. 560
- D. None of these
Answer: 560
622. The length, breadth and height of a cuboid are in the ratio 1 : 2 : 3. The length, breadth and height of the cuboid are increased by 100%, 200% and 200% respectively. Then the increase in the volume of the cuboid is
- A. 5 times
- B. 6 times
- C. 12 times
- D. 17 times
Answer: 17 times
Explanation: Let the original length, breadth and height of the cuboid be x, 2x and 3x units respectively. Then, original volume = (x × 2x × 3x) cu. units = 6x3 cu. units. New length = 200% of x = 2x, New breadth = 300% of 2x = 6x, New height = 300% of 3x = 9x. ∴ New volume = (2x × 6x × 9x) cu. units = 108 x3 cu. units. Increase in volume = (108 x3 – 6x3) cu. units = (102x3) cu. units ∴ Required ratio = 3 3 102 17. 6 x x =
Explanation: Let the original length, breadth and height of the cuboid be x, 2x and 3x units respectively. Then, original volume = (x × 2x × 3x) cu. units = 6x3 cu. units. New length = 200% of x = 2x, New breadth = 300% of 2x = 6x, New height = 300% of 3x = 9x. ∴ New volume = (2x × 6x × 9x) cu. units = 108 x3 cu. units. Increase in volume = (108 x3 – 6x3) cu. units = (102x3) cu. units ∴ Required ratio = 3 3 102 17. 6 x x =
623. Length of a rectangular solid is increased by 10% and breadth is decreased by 10%. Then the volume of the solid
- A. remains unchanged
- B. decreases by 1%
- C. decreases by 10%
- D. increases by 10%
Answer: decreases by 1%
624. A swimming pool 9 m wide and 12 m long is 1 m deep on the shallow side and 4 m deep on the deeper side. Its volume is :
- A. 208 m3
- B. 270 m3
- C. 360 m3
- D. 408 m3
Answer: 270 m3
625. The sum of perimeters of the six faces of a cuboid is 72 cm and the total surface area of the cuboid is 16 cm2. Find the longest possible length that can be kept inside the cuboid
- A. 5.2 cm
- B. 7.8 cm
- C. 8.05 cm
- D. 8.36 cm
Answer: 8.05 cm
626. The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5 5 cm. It surface area is
- A. 125 cm2
- B. 236 cm2
- C. 361 cm2
- D. 486 cm2
Answer: 236 cm2
627. Rita and Meeta both are having lunch boxes of a cuboidal shape. Length and breadth of Rita’s lunch box are 10% more than that of Meeta’s lunch box, but the depth of Rita’s lunch box is 20% less than that of Meeta’s lunch box. The ratio of the capacity of Rita’s lunch box to that of Meeta’s lunch box is
- A. 11 : 15 / 11: 15
- B. 15 : 11 / 15: 11
- C. 121 : 125 / 121: 125
- D. 125 : 121 / 125: 121
Answer: 121 : 125 / 121: 125
628. The water in a rectangular reservoir having a base 80 m by 60 m is 6.5 m deep. In what time can the water be emptied by a pipe of which the cross-section is a square of side 20 cm, if the water runs through the pipe at the rate of 15 km per hour?
- A. 26 hrs
- B. 42 hrs
- C. 52 hrs
- D. 65 hrs
Answer: 52 hrs
629. A rectangular tank is 225 m by 162 m at the base. With what speed must water flow into it through an aperture 60 cm by 45 cm so that the level may be raised 20 cm in 5 hours?
- A. 5000 m/hr
- B. 5200 m/hr
- C. 5400 m/hr
- D. 5600 m/hr
Answer: 5400 m/hr
630. Water enters a 80 m × 40 m rectangular tank through a pipe whose opening is 40 sq. cm, at 10 km/hr. By how much does the water level rise in half an hour?
- A. 3 cm 2
- B. 4 cm 9
- C. 5 cm 8
- D. None of these
Answer: 5 cm 8
631. A river 2.5 m deep and 45 m wide flows at 3.6 km per hour. How much water enters the sea per minute?
- A. 6650 cu. m
- B. 6750 cu. m
- C. 6850 cu. m
- D. 6950 cu. m
Answer: 6750 cu. m
632. A cistern, open at the top, is to be lined with sheet of lead which weights 27 kg/m2. The cistern is 4.5 m long and 3 m wide and holds 50 m3. The weight of lead required is
- A. 1660.5 kg
- B. 1764.5 kg
- C. 1860.5 kg
- D. 1864.5 kg
Answer: 1864.5 kg
633. A plot of land in the form of a rectangle has dimensions 240 m × 180 m. A drainlet 10 m wide is dug all around it (outside) and the earth dug out is evenly spread over the plot, increasing its surface level by 25 cm. The depth of the drainlet is
- A. 1.223 m
- B. 1.225 m
- C. 1.227 m
- D. 1.229 m
Answer: 1.227 m
634. A rectangular tank measuring 5 m × 4.5 m × 2.1 m is dug in the centre of the field measuring 13.5 m by 2.5 m. The earth dug out is evenly spread over the remaining portion of the field. How much is the level of the field raised?
- A. 4 m
- B. 4.1 m
- C. 4.2 m
- D. 4.3 m
Answer: 4.2 m
635. A school room is to be built to accommodate 70 children so as to allow 2.2 m2 of floor and 11 m3 of space for each child. If the room be 14 metres long, what must be its breadth and height?
- A. 11 m, 4 m
- B. 11 m, 5 m
- C. 12 m, 5.5 m
- D. 13 m, 6 m
Answer: 11 m, 5 m
636. A swimming bath is 24 m long and 15 m broad. When a number of men dive into the bath, the height of the water rises by 1 cm. If the average amount of water displaced by one of the men be 0.1 cu. m, how many men are there in the bath?
- A. 32
- B. 36
- C. 42
- D. 46
Answer: 36
637. 50 men dive into a water tank 40 m long and 20 m wide. If each man displaces 4 m³ of water on average, by how much does the water level rise?
- A. 20 cm
- B. 25 cm
- C. 35 cm
- D. 50 cm
Answer: 25 cm
638. How many bricks of 25 cm × 12.5 cm × 7.5 cm are needed for a wall 6 m long, 5 m high and 0.5 m thick, if mortar takes up 5% of the wall's volume?
- A. 3040
- B. 5740
- C. 6080
- D. 8120
Answer: 6080
639. How many bricks, each measuring 25 cm × 11.25 cm × 6 cm, will be needed to build a wall 8 m × 6 m × 22.5 cm?
- A. 5600
- B. 6000
- C. 6400
- D. 7200
Answer: 6400
640. The volume of a rectangular solid is 210 cm3 and the surface area is 214 cm2. If the area of the base is 42 cm2, then the edges of the rectangular solid are
- A. 3, 4 and 5 cm
- B. 4, 5 and 6 cm
- C. 5, 6 and 7 cm
- D. 6, 6 and 8 cm
Answer: 5, 6 and 7 cm