Question

Find the surface area of a sphere with a diameter of 40 inches. Leave your answer in terms of pi.(1 point)
The surface area is

Answer 1

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

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

where \( r \) is the radius of the sphere. The diameter of the sphere is 40 inches, so the radius \( r \) is half of that:

\[
r = \frac{40}{2} = 20 \text{ inches}
\]

Now, we can substitute the radius into the surface area formula:

\[
A = 4\pi (20)^2
\]

Calculating \( (20)^2 \):

\[
(20)^2 = 400
\]

Now substituting this value back into the surface area formula:

\[
A = 4\pi (400)
\]

\[
A = 1600\pi
\]

Thus, the surface area of the sphere is

\[
\boxed{1600\pi} \text{ square inches.}
\]