Question

The area in terms of piiswa mi?The approximated value for the area isA circle has a radius of 3 miles. Use the work shownbelow to identify the area in terms of pi and theapproximate area of the circle. Use 3.14 form and roundthe answer to the nearest tenth.A=²A = 2(3 mi)?A = 3.14(9 mi)IntroDone

Answer 1

We have to find the area of a circle with radius r = 3 miles.

The formula for the area of a circle (A) is:

`A=\pi r^2`

Then, if we replace with r = 3 miles, we get:

`\begin{gathered} A=\pi(3mi)^2 \\ A=\pi\cdot9mi^2 \\ A=9\pi\text{ square miles} \end{gathered}`

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:

`\begin{gathered} A=9\pi \\ A\approx9\cdot3.14 \\ A\approx28.3\text{ mi}^2 \end{gathered}`

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