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

The surface area \( S \) of a sphere is given by the formula:

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

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

Given that the diameter of the sphere is 30 inches, we can find the radius:

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

Now, we can substitute the value of \( r \) into the surface area formula:

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

Calculating \( (15)^2 \):

\[
(15)^2 = 225
\]

Now substitute this back into the surface area equation:

\[
S = 4\pi \times 225 = 900\pi
\]

Thus, the surface area of the sphere is:

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