Question

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

900 pi in.^2

225 pi in.^2

2,826 pi in.^2

3,600 pi 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.

Given that the diameter of the sphere is 30 inches, you can find the radius by dividing the diameter by 2:

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

Now, plug the radius into the surface area formula:

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

Calculating \( (15)^2 \):

\[
(15)^2 = 225
\]

Now substitute that back into the surface area formula:

\[
\text{Surface Area} = 4 \pi \times 225 = 900 \pi \text{ in.}^2
\]

Thus, the surface area of the sphere is:

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