Surface Areas & Volumes: Class 10 Previous Year Questions

Surface Areas & Volumes questions asked in CBSE board exams

Repeated questions first. Open the free app to see each question as it appeared in the paper, with its marking scheme.

1. A wooden article was made by scooping out a hemisphere (of same diameter) from one end of a solid cylinder as shown in the given figure. If the height of the cylinder is 10 cm and the diameter of the cylinder is 14 cm, find the total surface area of the remain…
   Board 20255 markslong answer
2. (a) A toy is in the form of a cone surmounted on a hemisphere. The cone and hemisphere have the same radii. The height of the conical part of the toy is equal to the diameter of its base. If the radius of the conical part is 5 cm, find the volume of the toy. O…
   Board 20255 markslong answer
3. | P a g e 15. A cone and a cylinder have the same base radius and volume. The (height of cone : height of cylinder) is : (A) 1 : 1 (B) 3 : 1 (C) 1 : 3 (D) 3 : 2 8| P a g e 16. = l + f1 : (A) (B) (C) (D) 17. = = a : (A) 3a (B) 2a (C) a (D) 0 18. : (A) 6 (B) 18 …
   Board 20251 markMCQ
4. For which of the following solids is the lateral / curved surface area and total surface area the same ? (A) Cube (B) Cuboid (C) Hemisphere (D) Sphere
   Board 20251 markMCQ
5. | P a g e 18. In a random experiment of throwing a die, which of the following is a sure event ? (A) Getting a number between 1 and 6 (B) Getting an odd number < 7 (C) Getting an even number < 7 (D) Getting a natural number < 7 12| P a g e (A) (R) (A), (B), (C…
   Board 20251 markAssertion-Reason
6. (A) A solid is in the form of a cylinder with hemi-spherical ends of same radi. The total height of the solid is 20 cm and the diameter of the cylinder is 14 cm. Find the surface area of the solid. (B) A juice glass is cylindrical in shape with hemi-spherical …
   Board 20243 marksshort answer
7. Page 17 35. (a) 5 A textile industry runs in a shed. This shed is in the shape of a cuboid surmounted by a half cylinder. If the base of the industry is of dimensions 14 m × 20 m and the height of the cuboidal portion is 7 m, find the volume of air that the in…
   Board 20245 markslong answer
8. A vessel is in the form of a hemispherical bowl surmounted by a hollow cylinder of same diameter. The diameter of the hemispherical bowl is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. Also, find the volume of t…
   Board 20235 markslong answer
9. The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. The diameter of its circular base is : (a) 2 cm (b) 1 cm (c) 4 cm (d) 7 cm
   Board 20231 markMCQ
10. 3 cubes each of 8 cm edge are joined end to end. Find the total surface area of the cuboid so formed. 4.··-, PQR 20 c- PA BAD=55DBC 55 31Tfa-2 20 - 30 30 - 40 50 - 60 40 - 50 60 - 70 25 30 42 45 : 35 6. 7.
    Board 20221 markvery short
11. (a) A spherical glass vessel has a cylindrical neck 8 cm long and 1 cm in radius. The radius of the spherical part is 9 cm. Find the amount of water (in litres) it can hold, when filled completely. 4 OR (b) From a solid cylinder, whose height is 2·4 cm and dia…
    Board 20221 markvery short
12. A solid cuboidal toy is made of wood. It has five cone shaped cavities to hold toy carrots. The dimensions of the toy are cuboid - 10 cm × 10 cm × 8 cm. Each cone carved out - Radius = 2.1 cm and Height = 6 cm. (1) Find the volume of wood carved out to make fi…
    Board 20221 markvery short
13. A solid metallic sphere of radius 3 cm is melted and recast into the shape of a solid cylinder of radius 2 cm. Find the height of the cylinder.
    Board 20221 markvery short
14. The largest possible hemisphere is drilled out of a wooden cubical block of side 21cm such that the base of the hemisphere is on one of the faces of the cube. Then, find i. the volume of the wood left in the block. ii. the total surface area of the remaining s…
    Sample paper 2026-275 markslong answer
15. g p p p of contacts as A and B, are inclined to each other at angle of 80°, then ∠AOB is equal to (A) 60° (B) 70° (C) 80° (D)100° 1 Two cubes each of volume 64cm3 are joined end to end to form a cuboid The
    Sample paper 2026-271 markMCQ
16. Two cubes each of volume 64cm are joined end to end to form a cuboid. The total surface area of the resulting cuboid is (A) 128 cm2 (B) 160 cm2 (C) 176 cm2 (D) 192 cm2 1 Assertion-Reason Based Questions Directions: Questions number 19 and 20 are Assertion and …
    Sample paper 2026-271 markAssertion-Reason

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