Question

Item 16 A sphere has a radius of 8 centimeters. A second sphere has a radius of 2 centimeters. What is the difference of the volumes of the spheres?

Answer 1

`672\pi \text{ cm}^3`.

Explanation:

We have been given that a sphere has a radius of 8 centimeters. A second sphere has a radius of 2 centimeters. We are asked to find the difference of the volumes of the spheres.

We will use volume formula of sphere to solve our given problem.

`\text{Volume of sphere}=(4)/(3)\pi r^3`, where r is radius of sphere.

The difference of volumes would be volume of larger sphere minus volume of smaller sphere.

`\text{Difference of volumes}=(4)/(3)\pi(\text{8 cm})^3-(4)/(3)\pi(\text{2 cm})^3`

`\text{Difference of volumes}=(4)/(3)\pi(512)\text{ cm}^3-(4)/(3)\pi(8)\text{ cm}^3`

`\text{Difference of volumes}=(4)/(3)\pi(512-8)\text{ cm}^3`

`\text{Difference of volumes}=4\pi(168)\text{ cm}^3`

`\text{Difference of volumes}=672\pi\text{ cm}^3`

Therefore, the difference between volumes of the spheres is
`672\pi \text{ cm}^3`.