Question

Solve. Use 3.14 for pi.
A radio station is allowed by the FCC to broadcast over an area with a radius of 208 mi. How much area is​ this?

Answers

GPT-4o mini
To find the area of the circular region that the radio station can broadcast over, you can use the formula for the area \( A \) of a circle:

\[
A = \pi r^2
\]

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

Given:
- \( r = 208 \) miles
- \( \pi \approx 3.14 \)

Now plug in the values:

\[
A = 3.14 \times (208)^2
\]

First, calculate \( (208)^2 \):

\[
(208)^2 = 43264
\]

Now plug that back into the area formula:

\[
A = 3.14 \times 43264
\]

Now calculate the area:

\[
A \approx 3.14 \times 43264 \approx 135761.76
\]

Therefore, the area covered by the radio station is approximately \( 135,761.76 \) square miles.