Question

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

Pi feet cubed

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. Since the diameter of the sphere is 12 feet, 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 \( (6 \text{ ft})^3 \):

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

Now substituting that back into the volume formula:

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

Calculating \( \frac{4}{3} \times 216 \):

\[
\frac{4 \times 216}{3} = \frac{864}{3} = 288
\]

Thus, the volume of the sphere is:

\[
V = 288\pi \text{ ft}^3
\]

So the exact value of the volume in terms of Pi is:

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