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AleksAgata [21]
3 years ago
5

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 vol

umes of the spheres?
Mathematics
1 answer:
Zigmanuir [339]3 years ago
3 0

Answer:

672\pi \text{ cm}^3.

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.

\text{Volume of sphere}=\frac{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}=\frac{4}{3}\pi(\text{8 cm})^3-\frac{4}{3}\pi(\text{2 cm})^3

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

\text{Difference of volumes}=\frac{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.

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