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
𝜋

in
.
2
900 pi inches squared

3,600π in.2
3
,
600
𝜋

in.
2
3,600 pi inches squared

225π in.2
225
𝜋

in.
2
225 pi inches squared

2,826π in.2

Answer 1

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

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

where \( A \) is the surface area and \( r \) is the radius of the sphere.

First, you need to determine the radius from the diameter. Given that the diameter is 30 inches, the radius \( r \) is:

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

Now, substitute \( r = 15 \) inches into the surface area formula:

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

Calculating \( (15)^2 \):

\[
(15)^2 = 225
\]

Now substitute this value back into the equation for \( A \):

\[
A = 4\pi (225) = 900\pi
\]

Thus, the surface area of the sphere is:

\[
\boxed{900\pi} \text{ in}^2
\]

The correct response is \( 900\pi \text{ in}^2 \).