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Class 10

Explore popular questions from Surface Areas and Volumes for Class 10. This collection covers Surface Areas and Volumes previous year Class 10 questions hand picked by experienced teachers.

Surface Areas and Volumes

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Q 1. A hemisphere and a cone have equal bases. If their height are also equal, then what is the ratio of their curved surfaces:

A

1 : 3

B

2 : 3

√2 : 1

D

None of these

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Q 2. A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?

3 : 1 : 2

B

1 : 2 : 3

C

4 : 5 : 6

D

2 : 3 : 1

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Q 3. If {tex} r _ { 1 } {/tex} and {tex} r _ { 2 } {/tex} denote the radii of the circular bases of the frustrum of a cone such that {tex} r _ { 1 } > r _ { 2 } , {/tex} then write the ratio of the height of the cone of which the frustrum is a part to the height of the frustrum.

{tex} \frac { r _ { 1 } } { r _ { 1 } + r _ { 2 } } {/tex}

B

{tex} \frac { r _ { 1 } } { r _ { 1 } - r _ { 2 } } {/tex}

C

{tex} \sqrt { 2 }: 1 {/tex}

D

{tex} \sqrt { r _ { 1 } } / r _ { 2 } {/tex}

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Q 4. A metallic hemisphere is melted and recast in the shape of a cone with the same base radius {tex} R {/tex} as that of the hemisphere. If {tex} H {/tex} is the height of the cone, then the value of the {tex} H / R {/tex} is:

A

{tex} 1 / 2 {/tex}

B

{tex} 4 / 6 {/tex}

C

{tex} 1 / 3 {/tex}

{tex} 2 / 1 {/tex}

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Q 5. For the figure shown below match the column:

{tex}(\mathrm A) - (\mathrm Q ) {/tex}

B

{tex} ( \mathrm { B } ) - ( \mathrm { R } ) {/tex}

C

{tex} ( \mathrm { C } ) - ( \mathrm { S } ) {/tex}

D

{tex} (\mathrm D ) - (\mathrm P ) {/tex}

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Q 6. There is a cylinder circumscribing the hemisphere such that their bases are common. The ratio of their volume is

A

1 : 3

B

1 : 2

2 : 3

D

3 : 4

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Q 7. The total surface area of a cube is numerically equal to the surface area of a sphere then the ratio of their volume is

A

{tex} \frac { \pi } { 6 } {/tex}

{tex} \sqrt { \frac { \pi } { 6 } } {/tex}

C

{tex} \frac { \pi } { 216 } {/tex}

D

{tex} \sqrt { \frac { 6 } { \pi } } {/tex}

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Q 8. If length, breadth and height of a cuboid is increased by {tex} x \% , y \% {/tex} and {tex} z \% {/tex} respectively. Then its volume is increased by:

{tex} \left[ x + y + z + \frac { x y + x z + y z } { 100 } + \frac { x y z } { ( 100 ) ^ { 2 } } \right] \% {/tex}

B

{tex} \left[ x + y + z + \frac { x y + x z + y z } { 100 } \right] \% {/tex}

C

{tex} \left[ x + y + z + \frac { x y z } { ( 100 ) ^ { 2 } } \right] \% {/tex}

D

None of these

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Q 9. Find the volume of a frustum of a cone whose height is {tex} 14 \mathrm { cm } {/tex} and the diameters of the circular base and top are {tex} 12 \mathrm { cm } {/tex} and {tex} 6 \mathrm { cm } {/tex} respectively

A

{tex} 896 \mathrm { cm } ^ { 3 } {/tex}

B

{tex} 1028 \mathrm { cm } ^ { 3 } {/tex}

{tex} 924 \mathrm { cm } ^ { 3 } {/tex}

D

{tex} 1236 \mathrm { cm } ^ { 3 } {/tex}

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Q 10. {tex}748{/tex} cubic cm of metal is used to make a metallic cylindrical pipe of length {tex} 14 \mathrm { cm } {/tex} and external radius {tex} 9 \mathrm { cm } . {/tex} Find its thickness

A

{tex} 2 \mathrm { cm } {/tex}

B

{tex} 2.5 \mathrm { cm } {/tex}

C

{tex} 1.5 \mathrm { cm } {/tex}

{tex} 1 \mathrm { cm } {/tex}

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Q 11. A hollow sphere of internal and external diameters {tex} 4 \mathrm { cm } {/tex} and {tex} 8 \mathrm { cm } {/tex} respectively is melted into a cone of base diameter {tex} 8 \mathrm { cm } . {/tex} Find the height of the cone

{tex} 14 \mathrm { cm } {/tex}

B

{tex} 12 \mathrm { cm } {/tex}

C

{tex} 16 \mathrm { cm } {/tex}

D

None of these

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Q 12. A cylindrical pencil sharpened at one edge is the combination of :

a cone and a cylinder

B

frustum of a cone and a cylinder

C

a hemisphere and a cylinder

D

two cylinders

Explanation

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Q 13. A surahi is the combination of :

a sphere and a cylinder

B

a hemisphere and a cylinder

C

two hemispheres

D

a cylinder and a cone

Explanation

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Q 14. A plumbline (Sahul) is the combination of :

A

a cone and a cylinder

a hemisphere and a cone

C

frustum of a cone and a cylinder

D

sphere and cylinder

Explanation

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Q 15. A hollow cube of internal edge {tex} 22 \mathrm { cm } {/tex} is filled with spherical marbles of diameter {tex} 0.5 \mathrm { cm } {/tex} and it is assumed that {tex} \frac { 1 } { 8 } {/tex} space of the cube remains unfilled. Then the number of marbles that the cube can accommodate is :

142296

B

142396

C

142496

D

142596

Explanation



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Q 16. A medicine-capsule is in the shape of a cylinder of diameter {tex} 0.5 \mathrm { cm } {/tex} with two hemispheres stuck to each to its ends. The length of entire capsule is {tex} 2 \mathrm { cm } . {/tex} The capacity of the capsule is :

{tex} 0.36 \mathrm { cm } ^ { 3 } {/tex}

B

{tex} 0.35 \mathrm { cm } ^ { 3 } {/tex}

C

{tex} 0.34 \mathrm { cm } ^ { 3 } {/tex}

D

{tex} 0.33 \mathrm { cm } ^ { 3 } {/tex}

Explanation

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Q 17. If two solid hemispheres of same base radius ' {tex} r {/tex} ' are joined together along their bases, then curved surface area of this new solid is:

{tex} 4 \pi r ^ { 2 } {/tex}

B

{tex} 6 \pi r ^ { 2 } {/tex}

C

{tex} 3 \pi r {/tex}

D

{tex} 8 \pi r^2 {/tex}

Explanation

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Q 18. In a right circular cone, the cross-section made by a plane parallel to the base is a :

circle

B

frustum of a cone

C

sphere

D

hemisphere

Explanation

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Q 19. Volumes of two spheres are in the ratio {tex} 64: 27 . {/tex} The ratio of their surface areas is :

A

3:4

B

4:3

C

9:16

16:9

Explanation

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Q 20. The surface areas of two spheres are in the ratio 16: 9 . The ratio of their volumes is:

{tex}64:27 {/tex}

B

{tex}16:9 {/tex}

C

{tex}4:3 {/tex}

D

{tex} 16 ^ { 3 }: 9 ^ { 3 } {/tex}

Explanation


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Q 21. A metallic spherical shell of internal and external diameters {tex} 4 \mathrm { cm } {/tex} and {tex} 8 \mathrm { cm } {/tex}, respectively, is melted and recast into the form of a cone of base diameter {tex} 8 \mathrm { cm } {/tex}. The height of the cone is:

A

{tex} 12 \mathrm { cm } {/tex}

{tex} 14 \mathrm { cm } {/tex}

C

{tex} 15 \mathrm { cm } {/tex}

D

{tex} 18 \mathrm { cm } {/tex}

Explanation

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Q 22. A solid piece of iron in the form of a cuboid of dimensions {tex} 49 \mathrm { cm } \times 33 \mathrm { cm } \times 24 \mathrm { cm } , {/tex} is moulded to form a solid sphere. The radius of the sphere is :

{tex} 21 \mathrm { cm } {/tex}

B

{tex} 23 \mathrm { cm } {/tex}

C

{tex} 25 \mathrm { cm } {/tex}

D

{tex} 19 \mathrm { cm } {/tex}

Explanation


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Q 23. A mason constructs a wall of dimensions {tex} 270 \mathrm { cm } \times {/tex} {tex} 300 \mathrm { cm } \times 350 \mathrm { cm } {/tex} with the bricks each of size {tex} 22.5 \mathrm { cm } \times 11.25 \mathrm { cm } \times 8.75 \mathrm { cm } {/tex} and it is assumed that {tex} 1 / 8 {/tex} space is covered by the mortar. Then the number of bricks used to construct the wall is:

A

11100

11200

C

11000

D

11300

Explanation


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Q 24. Twelve solid sphere of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is :

A

{tex} 4 \mathrm { cm } {/tex}

B

{tex} 3 \mathrm { cm } {/tex}

{tex} 2 \mathrm { cm } {/tex}

D

{tex} 6 \mathrm { cm } {/tex}

Explanation

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Q 25. A rectangular sheet of paper {tex} 40 \mathrm { cm } \times 22 \mathrm { cm } , {/tex} is rolled to form a hollow cylinder of height {tex} 40 \mathrm { cm } {/tex}. The radius of the cylinder (in {tex} \mathrm { cm } ) {/tex} is :

{tex}3.5{/tex}

B

{tex}7{/tex}

C

{tex} \frac { 80 } { 7 } {/tex}

D

{tex}5{/tex}

Explanation