CBSE Class 10 Mathematics Surface Areas and Volumes MCQs Set 12

INTEGRATED (MIXED) QUESTIONS

Question. Three cubes each of volume 216 \( m^3 \) are joined end to end. The surface area of the resulting solid is
(a) 216 \( m^2 \)
(b) 480 \( m^2 \)
(c) 432 \( m^2 \)
(d) 504 \( m^2 \)
Answer: (d) 504 \( m^2 \)

Question. A spherical ball of lead, 3 cm in diameter is melted and recast into three spherical balls. The diameter of two of the balls are 1.5 cm and 2 cm respectively. The diameter of the third balls is
(a) 2.4 cm
(b) 2.5 cm
(c) 2.7 cm
(d) 2.8 cm
Answer: (b) 2.5 cm

Question. The radii of the circular ends of a bucket of height 40 cm are 24 cm and 15 cm. The slant height (in cm) of the bucket is 
(a) 51
(b) 49
(c) 43
(d) 41
Answer: (d) 41

Question. A solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the radius of each ball is
(a) 3 cm
(b) 5 cm
(c) 6 cm
(d) 7 cm
Answer: (b) 5 cm

Question. In a box whose dimensions are 12 cm \( \times \) 4 cm \( \times \) 3 cm, the length of the longest stick that can be placed is
(a) 12 cm
(b) 11 cm
(c) 10 cm
(d) 13 cm
Answer: (d) 13 cm

Question. Two cubes have their volume in the ratio 1 : 64. The ratio of their surface areas is
(a) 1:4
(b) 1:8
(c) 1:16
(d) 1:64
Answer: (c) 1:16

Question. The ratio of the volume of a cube to that of a sphere which will exactly fit inside cube is [\( \pi = \frac{22}{7} \)]
(a) 2:1
(b) 21:11
(c) 22:7
(d) 7:22
Answer: (b) 21:11

Question. A solid is hemispherical at the bottom and conical (of same radius) above it. If the surface areas of the two parts are equal, then the ratio of the radius and slant height of the conical part is
(a) 1:3
(b) 1:2
(c) 1:4
(d) 1:6
Answer: (b) 1:2

Question. Given that 1 cu cm of marble weighs 25 g. The weight of a marble block 28 cm in width and 5 cm thick is 112 kg. Then the length of the marble block is
(a) 24 cm
(b) 30 cm
(c) 32 cm
(d) 36 cm
Answer: (c) 32 cm

Question. Two cubes each of 10 cm edge are joined end to end. The surface area of the resulting cuboid is
(a) 1200 \( cm^2 \)
(b) 1000 \( cm^2 \)
(c) 800 \( cm^2 \)
(d) 1400 \( cm^2 \)
Answer: (b) 1000 \( cm^2 \)

Question. A rectangular sheet of paper 44 cm \( \times \) 18 cm is rolled along its length and a cylinder is formed. The volume of the cylinder so formed is equal to [take \( \pi = \frac{22}{7} \)]
(a) 2772 \( cm^3 \)
(b) 2506 \( cm^3 \)
(c) 2460 \( cm^3 \)
(d) 2672 \( cm^3 \)
Answer: (a) 2772 \( cm^3 \)

Question. If the radius and height of a cylinder are in the ratio 5:7 and its volume is 550 \( cm^3 \), then its radius is equal to [take \( \pi = \frac{22}{7} \)]
(a) 6 cm
(b) 7 cm
(c) 5 cm
(d) 10 cm
Answer: (c) 5 cm

Question. If the curved surface area of a solid right circular cylinder of height h and radius r is one-third of its total surface area, then
(a) \( h = \frac{1}{3}r \)
(b) \( h = \frac{1}{2}r \)
(c) \( h = r \)
(d) \( h = 2r \)
Answer: (b) \( h = \frac{1}{2}r \)

Question. A hollow cylindrical pipe is 21 cm long. If its outer and inner diameter are 10 cm and 6 cm respectively, then the volume of the metal used in making the pipe is [take \( \pi = \frac{22}{7} \)]
(a) 1048 \( cm^3 \)
(b) 1056 \( cm^3 \)
(c) 1060 \( cm^3 \)
(d) 1064 \( cm^3 \)
Answer: (b) 1056 \( cm^3 \)

Question. A cylinderical pencil sharpened at one edge is the combination of
(a) a cone and a cylinder
(b) frustum of a cone and a cylinder
(c) a hemisphere and a cylinder
(d) two cylinders
Answer: (a) a cone and a cylinder

Question. If the radius and slant height of a cone are in the ratio 4:7 and its curved surface area is 792 \( cm^2 \), then its radius is [take \( \pi = \frac{22}{7} \)]
(a) 10 cm
(b) 8 cm
(c) 12 cm
(d) 9 cm
Answer: (c) 12 cm

Question. A conical tent with base-radius 7 m and height 24 m is made from 5 m wide canvas. The length of the canvas used is [take \( \pi = \frac{22}{7} \)]
(a) 100 m
(b) 105 m
(c) 110 m
(d) 115 m
Answer: (c) 110 m

Question. If a spherical marble of radius 2.1 cm is put into a cylinderical cup full of water of radius 5 cm and height 6 cm, then the volume of the water that flows out of the cylinderical cup is
(a) 471.4 \( cm^3 \)
(b) 38.8 \( cm^3 \)
(c) 55.4 \( cm^3 \)
(d) 19.4 \( cm^3 \)
Answer: (b) 38.8 \( cm^3 \)

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) h cm
(c) 2r cm
(d) 2h cm
Answer: (c) 2r cm

Question. The total surface area of a solid hemisphere of radius 3.5 m is covered with canvas at the rate of Rs. 20 per square meter. The total cost to cover the hemisphere is [take \( \pi = \frac{22}{7} \)]
(a) Rs. 2210
(b) Rs. 2310
(c) Rs. 2320
(d) Rs. 2420
Answer: (b) Rs. 2310

Question. If the volume of a vessel in the form of a right circular cylinder is \( 448\pi \text{ cm}^3 \) and its height is 7 cm, then the curved surface area of the cylinderis
(a) \( 224\pi \text{ cm}^2 \)
(b) \( 212\pi \text{ cm}^2 \)
(c) \( 112\pi \text{ cm}^2 \)
(d) None of the options
Answer: (c) \( 112\pi \text{ cm}^2 \)

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 \( cm^3 \)
(b) 77.6 \( cm^3 \)
(c) 58.2 \( cm^3 \)
(d) 19.4 \( cm^3 \)
Answer: (d) 19.4 \( cm^3 \)

Question. If the volume and the surface area of a sphere are numerically equal, then the radius of the sphere is
(a) 0 unit
(b) 1 unit
(c) 2 units
(d) 3 units
Answer: (d) 3 units