Question

Find the volume of a sphere with a radius of 9 cm. Leave your answer in terms of pi.(

Answer 1

The formula for the volume \( V \) of a sphere is given by:

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

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

For a sphere with a radius of \( 9 \) cm, we substitute \( r = 9 \) into the formula:

\[
V = \frac{4}{3} \pi (9)^3
\]

First, calculate \( 9^3 \):

\[
9^3 = 729
\]

Now, substitute \( 729 \) back into the volume formula:

\[
V = \frac{4}{3} \pi (729)
\]

Now, perform the multiplication:

\[
V = \frac{4 \times 729}{3} \pi
\]

Now, divide \( 4 \times 729 \) by \( 3 \):

\[
4 \times 729 = 2916
\]

\[
\frac{2916}{3} = 972
\]

Thus, the volume of the sphere is:

\[
V = 972 \pi \text{ cm}^3
\]

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

\[
\boxed{972\pi} \text{ cm}^3
\]