Question

Find the surface area of a sphere with a diameter of 30 inches. Leave your answer in terms of pi.

225pi
900pi
3,600pi
2,826pi

Answer 1

To find the surface area \( S \) of a sphere, we use the formula:

\[
S = 4\pi r^2
\]

where \( r \) is the radius of the sphere. The radius is half of the diameter. Given that the diameter of the sphere is 30 inches, we can calculate the radius:

\[
r = \frac{30}{2} = 15 \text{ inches}
\]

Now, substituting the radius into the surface area formula:

\[
S = 4\pi (15)^2
\]

Calculating \( (15)^2 \):

\[
15^2 = 225
\]

Now we can substitute this back into the formula:

\[
S = 4\pi \cdot 225
\]

Calculate \( 4 \cdot 225 \):

\[
4 \cdot 225 = 900
\]

Thus, the surface area of the sphere is:

\[
S = 900\pi
\]

So, the final answer is:

\[
\boxed{900\pi}
\]