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: πr^{2}h (here r and h are radius and height of the cylinder respectively)

Volume of cylinder is: πr^{2}h

Let V_{1} be the volume of first cylinder

∴ V_{1} = π(r_{1})^{2}h_{1}

Let V_{2} be the volume of the cone.

∴ V_{2} = π(r_{2})^{2}h_{2}

∴ V_{1} : V_{2} = π(r_{1})^{2}h_{1} : π(r_{2})^{2}h_{2}

⇒ V_{1} : V_{2} = π × (3)^{2} × 2 : × π × (4)^{2} × 3

⇒ V_{1} : V_{2} = 18π : × 48π = 18:16 = 9:8

∴ V_{1} : V_{2} = 9:8

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

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