The volume of a cylinder is 30 pie 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? Choices:…

Question

asked Mar 19, 2021 111k views

1 Answer

Alina Li · Answer 1 · 2021-03-25T02:50:34+0000

Given:

The volume of a cylinder is
$30 \pi$ 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

$V=\pi r^2 h$

Since, volume of the cylinder is
$30 \pi$ , we get;

$30 \pi = \pi r^2 h$ -------(1)

Volume of the cone:

The formula to determine the volume of the cone is

$V=(1)/(3) \pi r^2 H$

Substituting
H=2h , we get;

$V=(1)/(3) \pi r^2 (2h)$

$V=(2)/(3) \pi r^2 h$

Substituting equation (1), we get;

$V=(2)/(3) (30 \pi)$

$V=20 \pi$

Thus, the volume of the cone is 20π

Hence, Option C is the correct answer.