Answer:
[tex]672\pi \text{ cm}^3[/tex].
Step-by-step 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.
[tex]\text{Volume of sphere}=\frac{4}{3}\pi r^3[/tex], where r is radius of sphere.
The difference of volumes would be volume of larger sphere minus volume of smaller sphere.
[tex]\text{Difference of volumes}=\frac{4}{3}\pi(\text{8 cm})^3-\frac{4}{3}\pi(\text{2 cm})^3[/tex]
[tex]\text{Difference of volumes}=\frac{4}{3}\pi(512)\text{ cm}^3-\frac{4}{3}\pi(8)\text{ cm}^3[/tex]
[tex]\text{Difference of volumes}=\frac{4}{3}\pi(512-8)\text{ cm}^3[/tex]
[tex]\text{Difference of volumes}=4\pi(168)\text{ cm}^3[/tex]
[tex]\text{Difference of volumes}=672\pi\text{ cm}^3[/tex]
Therefore, the difference between volumes of the spheres is [tex]672\pi \text{ cm}^3[/tex].
