CBSE Class 10 Mathematics Surface Areas and Volumes Worksheet Set B

Question. The volume of a cylinder is 448 p cm³ and height 7 cm. Find its lateral surface area and total surface area is
(a) 253 cm²
(b) 352 cm²
(c) 532 cm²
(d) 325 cm²

Answer: B

Question. The diameter of a garden roller is 1.4 m, and 2m long. How much area will it cover in 5 revolutions.
(a) 44 m²
(b) 140 m²
(c) 440 m²
(d) 220 m²

Answer: A

Question. If a sphere and a cube have equal surface areas, then the ratio of the diameter of the sphere to the edge of the cube is
(a) 1 : 2
(b) 2 : 1
(c) √≠: √6
(d) √6 : √≠

Answer: D

Question. Three identical cones with base radius r are placed on their bases so that each is touching the other two. The radius of the circle drawn through their vertices is –
(a) smaller than r
(b) equal to r
(c) larger than r
(d) depends on the height of the cones

Answer: C

Question. The diameter of hollow cone is equal to the diameter of a spherical ball. If the ball is placed at the base of the cone, what portion of the ball will be outside the cone?
(a) 50%
(b) less than 50%
(c) more than 50%
(d) 100%

Answer: C

Question. A slab of ice 8 inches in length, 11 inches in breadth, and 2 inches thick was melted and resolidified in the form of a rod of 8 inches diameter. The length of such a rod, in inches, is nearest to
(a) 3
(b) 3.5
(c) 4
(d) 4.5

Answer: B

Question. The internal and external diameter of a hollow hemispherical vessel are 42 cm and 45.5 cm. respectively. Find its capacity (volume) and also its outer curved surface area.
(a) 5.27 litres, 3253.25 cm²
(b) 5.20 litres, 3253.25 cm²
(c) 5.27 litres, 3200.18 cm²
(d) 5.27 litres, 3250.25 cm²

Answer: A

Question. If h, c, v are respectively the height, the C.S.A and the volume of a cone, find the value of 3πvh³ – c²h² + 9v²
(a) 1
(b) 2
(c) 0
(d) 3

Answer: C

Question. If h be the height and α the semi-vertical angle of a right circular cone, then its volume is given by
(a) (1/3)πh³ tan² α
(b) (1/3)πh² tan² α
(c) (1/3)πh² tan³ α
(d) (1/3)πh³ tan³ α

Answer: A

Question. Cubes A, B, C having edges of 18 cm, 24 cm and 30 cm respectively are melted and moulded into a new cube D. Find the edge of the bigger cube D.
(a) 32
(b) 28
(c) 39
(d) 36

Answer: D

Question. The height of a conical tent is 14 m and its floor area is 346.5 m². The length of canvas, 11m wide, required for it is.
(a) 490 m
(b) 525 m
(c) 665 m
(d) 860 m

Answer: B

Question. If a solid of one shape is converted to another, then the volume of the new solid
(a) remains same
(b) increases
(c) decreases
(d) can’t say

Answer: A

Question. Ratio of lateral surface areas of two cylinders with equal height is
(a) 1 : 2
(b) H : h
(c) R : r
(d) None of the options

Answer: C

Question. The volume of a largest sphere that can be cut from cylindrical log of wood of base radius 1m and height 4 m, is
(a) 16/3 ≠ m³
(b) 8/3 ≠ m³
(c) 4/3 ≠ m³
(d) 10/3 ≠ m³

Answer: C

Question. If four times the sum of the areas of two circular faces of a cylinder of height 8 cm is equal to twice the curve surface area, then diameter of the cylinder is
(a) 4 cm
(b) 8 cm
(c) 2 cm
(d) 6 cm

Answer: B

Question. A rectangular sheet of paper 40 cm × 22 cm, is rolled to form a hollow cylinder of height 40 cm. The radius of the cylinder (in cm) is
(a) 3.5
(b) 7
(c) 80/7
(d) 5

Answer: A

Question. A right circular cylinder has its height equal to two times its radius. It is inscribed in a right circular cone having its diameter equal to 10 cm and height 12 cm, and the axes of both the cylinder and the cone coincide. Then, the volume (in cm³) of the cylinder is approximately
(a) 107.5
(b) 118.6
(c) 127.5
(d) 128.7

Answer: C

Question. Ratio of volumes of two cylinders with equal height is
(a) H : h
(b) R : r
(c) R² : r²
(d) None of the options

Answer: C

Question. Ratio of volumes of two cones with same radii is
(a) h₁ : h₂
(b) s₁ : s₂
(c) r₁ : r₂
(d) None of the options

Answer: A

Question. Volume of a spherical shell is given by
(a) 4π (R² – r²)
(b) π (R³ – r³)
(c) 4π (R³ – r³)
(d) (4/3) π (R³ – r³)

Answer: D

Question. If the ratio of volumes of two cubes is 27 : 64, then the ratio of their surface area is:
(a) 3 : 4
(b) 4 : 3
(c) 9 : 16
(d) 16 : 9

Answer: C

Question. Volumes of two spheres are in the ratio 125 : 64. The ratio of their surface areas will be
(a) 5 : 4
(b) 25 : 16
(c) 16 : 25
(d) 125 : 64

Answer: B

Question. Given three cubes with integer side lengths, if the sum of surface areas of three cubes is 498 sq. cm, then the sum of the volumes of the cubes in all possible solutions is
(a) 731
(b) 495
(c) 1226
(d) None of the options

Answer: C

Question. Which one of the following is/are incorrect ?
(a) Total surface area of cuboid is 2(lb + bh + hl)
(b) Total surface area of a cube is 4l2
(c) Area of four walls = 2h (l + b)
(d) Area of four walls = Height × Perimeter of the room

Answer: B

Question. A Circular Cylinder can not be separated into
(a) circular end at the bottom
(b) curved surface
(c) circular end at the top
(d) None of the options

Answer: D

Question. Which one of the following is / are incorrect ?
(a) Total surface area of cylinder is 2πr² + 2πrh.
(b) Total surface area of a sphere is 4πr².
(c) Total surface area of cone is πr² + πrl.
(d) None of the options

Answer: D

Question. A solid metallic block of volume one cubic metre is melted and recast into the form of a rectangular bar of length 9 metres having a square base. If the weight of the block is 90 kg and biggest cube is cut off from the bar, then the weight of the cube is
(a) 6(1/3)kg
(b) 5(2/3)kg
(c) 4(2/3)kg
(d) 3(1/3)kg

Answer: D

Question. Consider a cuboid all of whose edges are integers and whose base is a square. Suppose the sum of all its edges is numerically equal to the sum of the areas of all its six faces. Then, the sum of all its edges is
(a) 12
(b) 18
(c) 24
(d) 36

Answer: C

Question. Shyam wants to make a solid brick shape structure from 400 wooden cubes of unit volume each. If the sides of the solid brick have the ratio 1 : 2 : 3, then the maximum number of cubes, which can be used, will be _______.
(a) 400
(b) 288
(c) 300
(d) 384

Answer: D

Question. The number of solid cones with integer radius and integer height each having its volume numerically equal to its total surface area is
(a) 0
(b) 1
(c) 2
(d) infinite

Answer: B

Question. A solid metallic cylinder of height 10 cm and diameter 14 cm is melted to make two cones in the proportion of their volumes as 3 : 4, keeping the height 10 cm, what would be the percentage increase in the flat surface area?
(a) 9
(b) 16
(c) 50
(d) 200

Answer: C

Question. Which one of the following is/ are made up of combinations of two or more of the basic solids?
(a) Buildings
(b) Funnel
(c) Monuments
(d) Test-tube

Answer: B

Question. Among the following, which one is/are correct?
(a) The slant height is the longest side of a pyramid.
(b) The section between the base and a plane parallel to the base of a solid is known as frustum.
(c) All the surfaces of a cuboid are square.
(d) For a cylinder, the top, the bottom and the walls of the cylinder determine the total surface area.

Answer: C

Question. If a marble of radius 2.1 cm is put into a cylindrical cup full of water of radius 5cm and height 6 cm, then how much water flows out of the cylindrical cup?
(a) 38.8 cm³
(b) 55.4 cm³
(c) 19.4 cm³
(d) 471.4 cm³

Answer: A

Question. A cubical ice-cream brick of edge 22 cm is to be distributed among some children by filling ice-cream cones of radius 2 cm and height 7 cm upto its brim. How many children will get the ice-cream cones?
(a) 163
(b) 263
(c) 363
(d) 463

Answer: C

Question. The base radii of a cone and a cylinder are equal. If their curved surface areas are also equal, then the ratio of the slant height of the cone to the height of the cylinder is
(a) 2 : 1
(b) 1 : 2
(c) 1 : 3
(d) 3 : 1

Answer: A

Question. If the perimeter of one face of a cube is 20 cm, then its surface area is
(a) 120 cm²
(b) 150 cm²
(c) 125 cm²
(d) 400 cm²

Answer: B

Question. A cube of side 12 cm is painted red on all the faces and then cut into smaller cubes, each of side 3 cm. What is the total number of smaller cubes having none of their faces painted?
(a) 16
(b) 8
(c) 12
(d) 24

Answer: B

Question. If the diameter of the sphere is doubled, the surface area of the resultant sphere becomes x times that of the original one, then x would be
(a) 2
(b) 3
(c) 4
(d) 8

Answer: C

Question. If h be the height and α the semi-vertical angle of a right circular cone, then its volume is given by
(a) (1/3)πh³ tan² α
(b) (1/3)πh² tan² α
(c) (1/3)πh² tan³ α
(d) (1/3)πh³ tan³ α

Answer: A

Question. If the radius of the sphere is increased by 100%, the volume of the corresponding sphere is increased by
(a) 200%
(b) 500%
(c) 700%
(d) 800%

Answer: C

Question. A sphere is melted and half of the melted liquid is used to form 11 identical cubes, whereas the remaining half is used to form 7 identical smaller spheres. The ratio of the side of the cube to the radius of the new small sphere is
(a) (4/3)^1/3
(b) (8/3)^1/3
(c) (3)^1/3
(d) 2

Answer: B

Question. The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is
(a) 9.7 cm³
(b) 77.6 cm³
(c) 58.2 cm³
(d) 19.4 cm³

Answer: D

Question. If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is
(a) 4πr²
(b) 6πr²
(c) 3πr²
(d) 8πr²

Answer: A

Question. A right circular cylinder of radius r cm and height h cm (h > 2r) just encloses a sphere of diameter
(a) r cm
(b) 2r cm
(c) h cm
(d) 2h cm

Answer: B