Question

Solve. Use 3.14 for pi.
A radio station is allowed by the FCC to broadcast over an area with a radius of 233 mi. How much area is​ this?
Question content area bottom
Part 1
The area is
  
enter your response here misquared.
​(Simplify your answer. Type an integer or a decimal. Round to the nearest hundredth if​ needed.)

Answer 1

To find the area \( A \) of the circle (the area over which the radio station can broadcast), we can use the formula for the area of a circle:

\[
A = \pi r^2
\]

where \( r \) is the radius of the circle. Here, we're given that the radius \( r = 233 \) miles and \( \pi \approx 3.14 \).

Now, substituting in the values:

\[
A = 3.14 \times (233)^2
\]

First, calculate \( (233)^2 \):

\[
(233)^2 = 54289
\]

Now substitute back into the area formula:

\[
A = 3.14 \times 54289
\]

Next, multiply:

\[
A \approx 170,862.06
\]

So, the area over which the radio station can broadcast is approximately:

\[
\text{Area} \approx 170862.06 \text{ mi}^2
\]

Rounded to the nearest hundredth, the area is:

\[
\text{Area} = 170862.06 \text{ mi}^2
\]

You can enter \( 170862.06 \) as the final answer.