Q. 615.0( 1 Vote )

The radii of the base of a cylinder and a cone are in the ratio 3:4. If they have their height in the ratio 2:3, the ratio between their volumes is:
A. 12 cm

B. 14 cm

C. 15 cm

D. 18 cm

Answer :

Given: The radii of the base of a cylinder and a cone are in the ratio 3:4.


Heights of the base of a cylinder and a cone are in the ratio 2:3.


Volume of cylinder is: πr2h (here r and h are radius and height of the cylinder respectively)


Volume of cylinder is: πr2h


Let V1 be the volume of first cylinder


V1 = π(r1)2h1


Let V2 be the volume of the cone.


V2 = π(r2)2h2


V1 : V2 = π(r1)2h1 : π(r2)2h2


V1 : V2 = π × (3)2 × 2 : × π × (4)2 × 3


V1 : V2 = 18π : × 48π = 18:16 = 9:8


V1 : V2 = 9:8


That is the ratio of their volume is 9:8.

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