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?
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.
\[
A = \pi r^2
\]
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.