Question

A sphere has a diameter of 12 ft. What is the volume of the sphere? Give the exact value in terms of Pi.

Answer 1

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

\[
V = \frac{4}{3} \pi r^3
\]

where \( r \) is the radius of the sphere.

Given that the diameter of the sphere is 12 ft, we can find the radius by dividing the diameter by 2:

\[
r = \frac{12 \text{ ft}}{2} = 6 \text{ ft}
\]

Now we can substitute the radius into the volume formula:

\[
V = \frac{4}{3} \pi (6 \text{ ft})^3
\]

Calculating \( (6 \text{ ft})^3 \):

\[
(6 \text{ ft})^3 = 6^3 \text{ ft}^3 = 216 \text{ ft}^3
\]

Now substitute this value back into the volume formula:

\[
V = \frac{4}{3} \pi (216 \text{ ft}^3)
\]

Now multiply:

\[
V = \frac{4 \times 216}{3} \pi \text{ ft}^3 = \frac{864}{3} \pi \text{ ft}^3 = 288 \pi \text{ ft}^3
\]

Thus, the exact volume of the sphere in terms of \(\pi\) is:

\[
\boxed{288\pi \text{ ft}^3}
\]