Question

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

1 answer

The surface area \( S \) of a sphere can be calculated using the formula:

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

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

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

Now, substitute the radius into the surface area formula:

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

Calculating \( (20)^2 \):

\[ (20)^2 = 400 \]

Now substitute that value back into the formula:

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

Thus, the surface area of the sphere is:

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