Question

Find the surface area of a sphere with a diameter of 40 inches. Leave your answer in terms of pi.

Answer 1

To calculate the surface area of a sphere, we use the formula:

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

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

First, we need to find the radius. The diameter of the sphere is given as 40 inches, so we can find the radius by dividing the diameter by 2:

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

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

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

Calculating \( (20)^2 \):

\[
(20)^2 = 400
\]

Now, substituting back into the surface area formula:

\[
S = 4\pi \cdot 400
\]
\[
S = 1600\pi
\]

Thus, the surface area of the sphere is

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