Question

Find the surface area of a sphere with a diameter of 30 inches. Leave your answer in terms of pi.(1 point)
Responses

900π in.2
900 pi inches squared

225π in.2
225 pi inches squared

3,600π in.2
3,600 pi inches squared

2,826π in.2

Answer 1

To find the surface area of a sphere, you can use the formula:

\[
\text{Surface Area} = 4\pi r^2
\]

where \( r \) is the radius of the sphere. The diameter of the sphere is given as 30 inches, so the radius \( r \) is half of that:

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

Now, plug the radius into the surface area formula:

\[
\text{Surface Area} = 4\pi (15)^2
\]

Calculating \( (15)^2 \):

\[
(15)^2 = 225
\]

Now substitute this back into the formula:

\[
\text{Surface Area} = 4\pi \times 225
\]

Calculating \( 4 \times 225 \):

\[
4 \times 225 = 900
\]

Thus, we have:

\[
\text{Surface Area} = 900\pi \text{ in}^2
\]

Therefore, the surface area of the sphere is \( 900\pi \text{ in}^2 \).

The correct response is:

**900π in.²** (or **900 pi inches squared**)