Question

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: A.5 pie B. 15 pie C. 20 pie D. 45 pie E. 60 pie

Answer 1

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

$V=\frac{1}{3} \pi r^2 H$

Substituting $H=2h$, we get;

$V=\frac{1}{3} \pi r^2 (2h)$

$V=\frac{2}{3} \pi r^2 h$

Substituting equation (1), we get;

$V=\frac{2}{3} (30 \pi)$

$V=20 \pi$

Thus, the volume of the cone is 20π

Hence, Option C is the correct answer.