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# 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 cmB. 14 cmC. 15 cmD. 18 cm

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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