Question

A sphere has a radius of 5 in. A cone has a radius of 6 in. and a height of 8 in.

What is the difference in the volumes of the cone and the sphere, to the nearest cubic inch? Use 3.14 for r. Show your work.

Answer 1

The difference in volumes of the cone and the sphere is -222 in^3.

Step-by-step explanation:

To find the volume of the sphere, we use the formula:

Volume of sphere = 4/3 * pi * r^3

Substituting the radius 5 in, we get:

Volume of sphere = 4/3 * 3.14 * 5^3 = 523.33 in^3

To find the volume of the cone, we use the formula:

Volume of cone = 1/3 * pi * r^2 * h

Substituting the radius 6 in and height 8 in, we get:

Volume of cone = 1/3 * 3.14 * 6^2 * 8 = 301.44 in^3

The difference in volumes is:

Difference = Volume of cone - Volume of sphere = 301.44 in^3 - 523.33 in^3 = -221.89 in^3

To the nearest cubic inch, the difference in volumes of the cone and the sphere is -222 in^3.