The volume of a cylinder is 30pi cubic units. A cone shares the same base. The height of the cone is twice the height of the cylinder. What is the volume of the cone?
Write answers in terms of "pi" ex: 10pi cubic units

Step-by-step explanation:

Given:

The volume of a cylinder is 30π cubic units.

A cone shares the same base.

The height of the cone is twice the height of the cylinder.

We need to determine the volume of the cone.

Height of the Cone:

Let h denote the height of the cylinder.

Let H denote the height of the cone.

Since, it is given that, the height of the cone is twice the height of the cylinder, we have;

H=2h

Volume of the cylinder:

The formula to determine the volume of the cylinder is

V=πr^2h

Since, volume of the cylinder is 30π , we get;

30π=πr^2(1)

Volume of the cone:

The formula to determine the volume of the cone is

v=1/3πr^2H

Substituting H=2h , we get;

v=1/3πr^2(2h)

v=1/3πr^2h

Substituting equation (1), we get;

V=2/3(30π)

v=20π

Thus, the volume of the cone is 20π

The answer is 20pi

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