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. On a Sunday your parents took you to a fair. You could see lot of strawberry ice-cream for you. Based on the information given above, answer the following questions : (i) Find the length of the diagonal of Rubik's cube if each edge measures 6 cm. (ii) Find the…
   Board 20264 marksshort answer
2. Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is 160 cm2. Reason (R): The surface area of a cuboid of dimensions l × b × h is (lb + bh + hl). n
   Board 20261 markAssertion-Reason
3. A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter of the cylinder is 7 cm. Find Use ·= 22 the total volume of the solid. Page 9 of 16 31. (i) I · ) 32· ==8 =9 3200 (B·64064, 34.·A) gf (Basic P…
   Board 20263 marksshort answer
4. A hemispherical bowl is made of steel of thickness 1 cm. The outer radius of the bowl is 6 cm. The volume of steel used (in cm3) is : (A) 182 · 182 (B) 682 (C) (D) 17. (A) 43·4 (B) 42·4 (C) 44.2 (D) 49·3 18. 1, 24 25 : hk 15 (A) 25 10 (B) 25 11 (C) 25 (D) 25 (…
   Board 20261 markMCQ
5. A room is in the form of a cylinder surmounted by a hemispherical dome. The base radius of the hemisphere is half of the height of the cylindrical part. If the room contains m3 of air, find the height of the cylindrical part. (Use = ).
   Board 20253 marksshort answer
6. | P a g e 38. A skilled carpenter decided to craft a special rolling pin for the local baker. He carefully joined three cylindrical pieces of wood two small ones on the ends and one larger in the centre to create a perfect tool. The baker loved the rolling pin…
   Board 20254 marksshort answer
7. | P a g e 20. Assertion (A) : If we join two hemispheres of same radius along their bases, then we get a sphere. Reason (R): Total Surface Area of a sphere of radius r is 3 r2. 14| P a g e 5 - (VSA) , 2 5 2=10 21. x cos 60 + y cos 0 + sin 30 cot 45 = 5 , x + 2…
   Board 20251 markAssertion-Reason
8. Assertion (A) : Two cubes each of edge length 10 cm are joined together. The total surface area of newly formed cuboid is 1200 cm2. Reason (R) : Area of each surface of a cube of side 10 cm is 100 cm2.
   Board 20241 markAssertion-Reason
9. Page 21 37. The word ‘circus’ has the same root as ‘circle’. In a closed circular area, various entertainment acts including human skill and animal training are presented before the crowd. A circus tent is cylindrical upto a height of 8 m and conical above it.…
   Board 20244 marksshort answer
10. The difference between the outer and inner radii of a hollow right circular cylinder of length 14 cm is 1 cm. If the volume of the metal used in making the cylinder is 176 cm', find the outer and inner radii of the cylinder.
    Board 20243 marksshort answer
11. A solid sphere is cut into two hemispheres. The ratio of the surface areas of sphere to that of two hemispheres taken together, is : (a) 1:1 (b) 1 : 4 (c) 2 :3 (d) 3 :
    Board 20241 markMCQ
12. The volume of the largest right circular cone that can be carved out from a solid cube of edge 2 cm is : 4· 5· 8· 2· (a) (b) (c) cu cm cu cm cu cm (d) cu cm C3ABD/1 / 31 Page 5 16. 11 (a) (b) (c) (d) 36 36 36 17. (a) (0, 0) (b) (4, 0) (c) (-2, 0) (d) (- 6, 0) …
    Board 20241 markMCQ
13. tan ·+sec·-1 1+sin · 30. Prove that : tan 0-sec 0+1 cos 0 Page 15 31. (a) ·1408· 21 (b) TT , 3TSHT 3 1 (·= 3.14 1) 33.246024 () 60 Page 16
    Board 20233 marksshort answer
14. Curved surface area of a cylinder of height 5 cm is 94.2 cm2. Radius of the cylinder is (Take · = 3.14) 2cm (B) (A) 3 cm (C) (D) 2.9 cm 6 cm Page 7 11. 80, , : 12 27 57 75 80 (A) 10 -20 (B) 20 - 30 (C) 30 - 40 (D) 50 - 60 12. 7cm 24 cm· (A) 528 cm² (B) 1056 cm…
    Board 20231 markMCQ
15. (a) A room is in the form of cylinder surmounted by a hemi-spherical ·1408· cylindrical part. Find total height of the room if it contains 21 Take · = 22 of air. OR (b) An empty cone is of radius 3 cm and height 12 cm. Ice-cream is filled in it so that lower p…
    Board 20233 marksshort answer
16. JJJJ Page 21 37. In a coffee shop, coffee is served in two types of cups. One is cylindrical in shape with diameter 7 cm and height 14 cm and the other is hemispherical with diameter 21 cm. Based on the above, answer the following questions : (i) Find the area…
    Board 20234 marksshort answer
17. The curved surface area of a cone having height 24 cm and radius 7 cm, is (A) 528 cm2 (B) 1056 cm2 ·550cm² (C) (D) 500 cm2
    Board 20231 markMCQ
18. A solid metallic sphere of radius 10·5 cm is melted and recast into a number of smaller cones, each of radius 3·5 cm and height 3 cm. Find the number of cones so formed.
    Board 20221 markvery short
19. A solid piece of metal in the form of a cuboid of dimensions 1l cm × 7 cm × 7 cm is melted to form ·n' number of solid spheres of radii cm each. Find the value of n.
    Board 20221 markvery short
20. Case Study- 2 A ·circus' is a company of performers who put on shows of acrobats, clowns etc. to entertain people started around 250 years back, in open fields, now generally performed in tents. One such'Circus Tent'is shown below. The tent is in the shape of …
    Board 20221 markvery short

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