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Class 9

Explore popular questions from Surface Areas and Volumes for Class 9. This collection covers Surface Areas and Volumes previous year Class 9 questions hand picked by experienced teachers.

Surface Areas and Volumes

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Q 1. Two cubes each of volume {tex} 64 \mathrm { cm } ^ { 3 } {/tex} are joined end to end. Find the volume of the resulting cuboid.

A

{tex} 148 \mathrm { cm } ^ { 3 } {/tex}

{tex} 128 \mathrm { cm } ^ { 3 } {/tex}

C

{tex} 182 \mathrm { cm } ^ { 3 } {/tex}

D

{tex} 821 \mathrm { cm } ^ { 3 } {/tex}

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Q 2. A conical vessel whose internal radius is {tex} 5 \mathrm { cm } {/tex} and height {tex} 24 \mathrm { cm } {/tex} is full of water. The water is emptied into a cylindrical vessel with internal radius {tex} 10 \mathrm { cm } . {/tex} What is the height to which the water rises

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

B

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

C

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

D

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

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Q 3. Diagonal of a cube is {tex} \sqrt { 6 } \mathrm { cm } . {/tex} Then its lateral surface area is:

A

{tex} 6 \sqrt { 6 } \mathrm { cm } ^ { 2 } {/tex}

B

{tex} 36 \mathrm { cm } ^ { 2 } {/tex}

C

{tex} 12 \mathrm { cm } ^ { 2 } {/tex}

{tex} 8 \mathrm { cm } ^ { 2 } {/tex}

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Q 4. A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is {tex} 14 \mathrm { cm } {/tex} and the total height of the vessel is {tex} 13 \mathrm { cm } {/tex}, then what is the capacity of the vessel?

{tex} 1642.66 \mathrm { cm } ^ { 3 } {/tex}

B

{tex} 1462.66 \mathrm { cm } ^ { 3 } {/tex}

C

{tex} 1662.42 \mathrm { cm } ^ { 3 } {/tex}

D

{tex} 1246.26 \mathrm { cm } ^ { 3 } {/tex}

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Q 5. A cylinder of base diameter {tex} 8 \mathrm { cm } {/tex} and height {tex} 7 \mathrm { cm } {/tex} is dipped vertically one third in a bucket full of paints. How much area get painted?

{tex} 108.95 \mathrm { cm } ^ { 3 } {/tex}

B

{tex} 553.14 \mathrm { cm } ^ { 3 } {/tex}

C

{tex} 318.47 \mathrm { cm } ^ { 3 } {/tex}

D

{tex} 226.28 \mathrm { cm } ^ { 3 } {/tex}

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Q 6. {tex}12{/tex} spheres of the same size are made from melting a solid cylinder of {tex} 16 \mathrm { cm } {/tex} diameter and {tex} 2 \mathrm { cm } {/tex} height. The diameter of each sphere is

A

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

B

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

C

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

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

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Q 7. Match the following:

Column I Column II
(A) Volume of hollow cylinder (P) {tex} \sqrt { l ^ { 2 } + b ^ { 2 } + h ^ { 2 }}{/tex}
(B) Diagonal of cuboid (Q){tex} { \pi r ( l + r ) }{/tex}
(C) Volume of hemisphere (R) {tex}\pi h ( R ^ { 2 } - r ^ { 2 }{/tex}
(D) Total surface area of cone (S) {tex} \frac { 4 } { 3 } \pi ( \frac { r ^ { 3 } } { 2 }){/tex}

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

B

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

C

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

D

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

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Q 8. The number of solid spheres, each of diameter {tex} 6 \mathrm { cm } {/tex} that could be moulded to form a solid metal cylinder of height {tex} 45 \mathrm { cm } {/tex} and diameter {tex} 4 \mathrm { cm } {/tex} is

A

3

B

4

5

D

6

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Q 9. A solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then radius of the base of the cone is

{tex} 2 r {/tex}

B

{tex} 3 r {/tex}

C

{tex}r{/tex}

D

{tex}4r{/tex}

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Q 10. The diameter of a sphere is {tex} 6 \mathrm { cm } {/tex}. It is melted and drawn into a wire of diameter {tex} 2 \mathrm { mm } {/tex}. The length of wire is

A

{tex} 12 \mathrm { m } {/tex}

B

{tex} 18 \mathrm { m } {/tex}

{tex} 36 \mathrm { m } {/tex}

D

{tex} 66 \mathrm { m } {/tex}

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Q 11. The areas of three adjacent faces of a cuboid are a, b and c. If its volume is {tex} \mathrm V {/tex} then

A

{tex} \mathrm { V } = \mathrm { abc } {/tex}

{tex} \mathrm { V } ^ { 2 } = \mathrm { abc } {/tex}

C

{tex} \mathrm { V } = \mathrm { a } ^ { 2 } \mathrm { b } ^ { 2 } \mathrm { c } ^ { 2 } {/tex}

D

{tex} \sqrt { \mathrm { V } } = \mathrm { a } ^ { 2 } \mathrm { b } ^ { 2 } \mathrm { c } ^ { 2 } {/tex}

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Q 12. A basket ball is just packed in a cube of side {tex} 20 \mathrm { cm } , {/tex} then the surface area of the basket ball is:

A

{tex} 120 \mathrm { cm } ^ { 2 } {/tex}

B

{tex} 2400 \mathrm { cm } ^ { 2 } {/tex}

{tex} 400 \pi \mathrm { cm } ^ { 2 } {/tex}

D

{tex} 1256 \mathrm { cm } ^ { 2 } {/tex}

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Q 13. A conical vessel has a capacity of {tex}3.3 \mathrm{litres}{/tex} of milk. If the height of the vessel is {tex} 3.5 \mathrm { cm } , {/tex} then the diameter of the base is

A

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

B

{tex} 30 \mathrm { cm } {/tex}

C

{tex} 35 \mathrm { cm } {/tex}

{tex} 60 \mathrm { cm } {/tex}

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Q 14. Match the following:

Column I Column II
(A) Ratio of the volume of a cone and sphere if each has the same diameter and same height (P) 9:32
(B) The radii of two cones are in the ratio 2:1 and their volumes are equal,
then ratio of their heights is
(Q) 1:2
(C) If the heights of two right circular cones are in the ratio 1:2
and the perimeters of their bases are in the ratio 3:4, then ratio of their volume is
(R) 1:4
(D) A right circular cone and a right circular cylinder have equal base and equal height are in the ratio 5:12,
the ratio of the total surface area of the cylinder to that of the cone is
(S) 17:9

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

B

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

C

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

D

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

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Q 15. If 'l ', 'b' and 'h' of a cuboid are increased, decreased and increased by 1%, 3% and 2% respectively, then the volume of the cuboid ___________.

A

Increases

Decreases

C

Increases or decreases depending on original dimensions

D

Can't be calculated with given data

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Q 16. A cuboidal metal block of dimensions 20 cm {tex}\times{/tex} 16 cm {tex}\times{/tex} 12 cm weighs 6 kg. Find the weight of block of the same metal of size 10 cm {tex}\times{/tex} 8 cm {tex}\times{/tex} 8 cm.

A

3 kg

B

8 kg

C

7 kg

1 kg

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Q 17. The bottom, side and front areas of a rectangular box are known. The product of these areas is equal to

A

the volume of box

B

the square root of the volume

C

twice the volume

the square of the volume

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Q 18. A right circular cone has for its base a circle having he same radius as a given sphere. The volume of the cone is one half that of the sphere. The ratio of the altitude of the cone to the radius of its base is:

A

1 : 1

B

1 : 2

2 : 1

D

2 : 3