Question

A cone and a cylinder have the same radius and height. The volume of the cone is 100π (pi) cubic feet. What is the volume of the cylinder?

Answer 1

Answer:

The volume of the cylinder is $300\pi$ cubic feet.

Step-by-step explanation:

From Geometry we remember that volumes of a cone and a cylinder with the same radius ($R$), measured in feet, and height ($h$), measured in feet, are defined by the following equations:

Cone

$V_{co} = \frac{1}{3}\pi\cdot R^{2}\cdot h$ (1)

Cylinder

$V_{cy} = \pi\cdot R^{2}\cdot h$ (2)

The ratio of the volume of the cylinder to the volume of the cone is:

$\frac{V_{cy}}{V_{co}} = 3$ (3)

If we know that $V_{co} = 100\pi\,ft^{3}$, then the volume of the cylinder is:

$V_{cy} = 3\cdot V_{co}$

$V_{cy} = 300\pi\,ft^{3}$

The volume of the cylinder is $300\pi$ cubic feet.