We have to find the area of a circle with radius r = 3 miles.
The formula for the area of a circle (A) is:
[tex]A=\pi r^2[/tex]
Then, if we replace with r = 3 miles, we get:
[tex]\begin{gathered} A=\pi(3mi)^2 \\ A=\pi\cdot9mi^2 \\ A=9\pi\text{ square miles} \end{gathered}[/tex]
If we express the are in units of π, we have an area A = 9π square miles.
As π has infinite decimals, we have to approximate it use it in calculations. If we round π to 2 decimals, we get π ≈ 3.14.
If we use this approximation in our formula for the area, we get:
[tex]\begin{gathered} A=9\pi \\ A\approx9\cdot3.14 \\ A\approx28.3\text{ mi}^2 \end{gathered}[/tex]
Answer:
a) The area in terms of pi is 9π mi².
b) The approximate value of the area (rounded to the nearest tenth) is 28.3 mi²