CBSE Class 10 Mathematics Surface Areas and Volumes MCQs Set I

Question. The volume of a cube is \( 2744 \text{ cm}^3 \). Its surface area is
(a) \( 196 \text{ cm}^2 \)
(b) \( 1176 \text{ cm}^2 \)
(c) \( 784 \text{ cm}^2 \)
(d) \( 588 \text{ cm}^2 \)
Answer: B

Question. The ratio of the total surface area to the lateral surface area of a cylinder with base radius \( 80 \text{ cm} \) and height \( 20 \text{ cm} \) is
(a) \( 1 : 2 \)
(b) \( 2 : 1 \)
(c) \( 3 : 1 \)
(d) \( 5 : 1 \)
Answer: D

Question. The height of a cylinder is \( 14 \text{ cm} \) and its curved surface area is \( 264 \text{ cm}^2 \). The volume of the cylinder is
(a) \( 296 \text{ cm}^3 \)
(b) \( 396 \text{ cm}^3 \)
(c) \( 369 \text{ cm}^3 \)
(d) \( 503 \text{ cm}^3 \)
Answer: B

Question. The ratio of the volumes of two spheres is \( 8 : 27 \). The ratio between their surface areas is
(a) \( 2 : 3 \)
(b) \( 4 : 27 \)
(c) \( 8 : 9 \)
(d) \( 4 : 9 \)
Answer: D

Question. The radii of the base of a cylinder and a cone are in the ratio \( 3 : 4 \) and their heights are in the ratio \( 2 : 3 \), then ratio of their volumes is
(a) \( 9 : 8 \)
(b) \( 9 : 4 \)
(c) \( 3 : 1 \)
(d) \( 27 : 64 \)
Answer: A

Question. The base radius of the cylinder is \( 1\frac{2}{3} \) times its height. The cost of painting its C.S.A. at \( 2 \text{ paise/cm}^2 \) is \( rs 92.40 \). The volume of the cylinder is
(a) \( 80850 \text{ cm}^3 \)
(b) \( 88850 \text{ cm}^3 \)
(c) \( 80508 \text{ cm}^3 \)
(d) none of these
Answer: A

Question. A spherical ball of radius \( 3 \text{ cm} \) is melted and recast into three spherical balls. The radii of two of these balls are \( 1.5 \text{ cm} \) and \( 2 \text{ cm} \). The radius of the third ball is
(a) \( 1.5 \text{ cm} \)
(b) \( 2 \text{ cm} \)
(c) \( 3 \text{ cm} \)
(d) \( 2.5 \text{ cm} \)
Answer: D

Question. A circus tent is cylindrical up to a height of \( 4 \text{ m} \) and conical above it. If its diameter is \( 105 \text{ m} \) and its slant height is \( 40 \text{ m} \), the total area of canvas required to built the tent is
(a) \( 7920 \text{ m}^2 \)
(b) \( 7820 \text{ m}^2 \)
(c) \( 9720 \text{ m}^2 \)
(d) \( 2645 \text{ m}^2 \)
Answer: A

Question. A glass cylinder with diameter \( 20 \text{ cm} \) has water to a height of \( 9 \text{ cm} \). A metal cube of \( 8 \text{ cm} \) edge is immersed in it completely. The height by which water will rise in the cylinder is (Take \( \pi = 3.14 \))
(a) \( 1.6 \text{ cm} \)
(b) \( 2.5 \text{ cm} \)
(c) \( 1 \text{ cm} \)
(d) \( 2.6 \text{ cm} \)
Answer: A

Question. The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is \( 5 \text{ cm} \), then height of the cone is
(a) \( 10 \text{ cm} \)
(b) \( 15 \text{ cm} \)
(c) \( 18 \text{ cm} \)
(d) \( 24 \text{ cm} \)
Answer: B

Question. A cylindrical vessel \( 16 \text{ cm} \) high and \( 9 \text{ cm} \) as the radius of the base, is filled with sand. This vessel is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is \( 12 \text{ cm} \), the radius of its base is
(a) \( 12 \text{ cm} \)
(b) \( 18 \text{ cm} \)
(c) \( 36 \text{ cm} \)
(d) \( 48 \text{ cm} \)
Answer: B

Question. The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius \( 1 \text{ cm} \) and height \( 5 \text{ cm} \) is
(a) \( \frac{4}{3}\pi \text{ cm}^3 \)
(b) \( \frac{10}{3}\pi \text{ cm}^3 \)
(c) \( 5\pi \text{ cm}^3 \)
(d) \( \frac{20}{3}\pi \text{ cm}^3 \)
Answer: A

Question. \( 12 \) spheres of the same size are made from melting a solid cylinder of \( 16 \text{ cm} \) diameter and \( 2 \text{ cm} \) height. The diameter of each sphere is
(a) \( \sqrt{3} \text{ cm} \)
(b) \( 2 \text{ cm} \)
(c) \( 3 \text{ cm} \)
(d) \( 4 \text{ cm} \)
Answer: D

Question. A rectangular sheet of paper \( 44 \text{ cm} \times 18 \text{ cm} \) 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) \( 2772 \text{ cm}^3 \)
(b) \( 2506 \text{ cm}^3 \)
(c) \( 2460 \text{ cm}^3 \)
(d) \( 2672 \text{ cm}^3 \)
Answer: A

Question. A toy is in the form of a cone mounted on a hemisphere of radius \( 7 \text{ cm} \). The total height of the toy is \( 14.5 \text{ cm} \). Find the volume of the toy. (Take \( \pi = \frac{22}{7} \))
(a) \( \frac{539}{6} \text{ cm}^3 \)
(b) \( \frac{3311}{3} \text{ cm}^3 \)
(c) \( \frac{847}{6} \text{ cm}^3 \)
(d) \( 200 \text{ cm}^3 \)
Answer: B

Question. A cube whose edge is \( 20 \text{ cm} \) long, has circles on each of its faces painted black. What is the total area of the unpainted surface of the cube, if the circles are of the largest possible areas?
(a) \( 90.72 \text{ cm}^2 \)
(b) \( 256.72 \text{ cm}^2 \)
(c) \( 330.3 \text{ cm}^2 \)
(d) \( 514.28 \text{ cm}^2 \)
Answer: D

Question. In a swimming pool, base measuring \( 90 \text{ m} \times 40 \text{ m} \), \( 150 \) men take a dip. If the average displacement of water by a man is \( 8 \text{ m}^3 \), then rise in water level is
(a) \( 27.33 \text{ cm} \)
(b) \( 30 \text{ cm} \)
(c) \( 31.33 \text{ cm} \)
(d) \( 33.33 \text{ cm} \)
Answer: D

Question. The areas of three adjacent faces of a rectangular block are in the ratio of \( 2 : 3 : 4 \) and its volume is \( 9000 \text{ cu. cm} \), then the length of the shortest side is
(a) \( 10 \text{ cm} \)
(b) \( 12 \text{ cm} \)
(c) \( 15 \text{ cm} \)
(d) \( 18 \text{ cm} \)
Answer: C

Assertion & Reasoning Based MCQs

Directions (53 to 60) : In these questions, a statement of Assertion is followed by a statement of Reason is given.
Choose the correct answer out of the following choices :
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Question. Assertion : The sum of the length, breadth and height of a cuboid is \( 19 \text{ cm} \) and its diagonal is \( 5\sqrt{5} \text{ cm} \). Its surface area is \( 236 \text{ cm}^2 \).
Reason : The lateral surface area of a cuboid is \( 2(l + b)h \).
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.
Answer: B

Question. Assertion : If the areas of three adjacent faces of a cuboid are \( x, y, z \) respectively then the volume of the cuboid is \( \sqrt{xyz} \).
Reason : Volume of a cuboid whose edges are \( l, b \) and \( h \) is \( lbh \) units.
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.
Answer: A

Question. Assertion : The volume of a hall, which is \( 5 \) times as high as it is broad and \( 8 \) times as long as it is high, is \( 12.8 \text{ m}^3 \). The breadth of the hall is \( 25 \text{ cm} \).
Reason : The total surface area of a cuboid of length \( (l) \), breadth \( (b) \) and height \( (h) \) is \( 2[lb + bh + lh] \).
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.
Answer: D

Question. Assertion : From a solid cylinder, whose height is \( 12 \text{ cm} \) and diameter \( 10 \text{ cm} \) a conical cavity of same height and same diameter is hollowed out. Then, volume of the cone is \( \frac{2200}{7} \text{ cm}^3 \).
Reason : If a conical cavity of same height and same diameter is hollowed out from a cylinder of height \( h \) and base radius \( r \), then volume of the cone will be half of the volume of the cylinder.
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.
Answer: C​​​​​​​