Question

the area of a circle is 4π square miles. what is the radius?
a = 4π mi²
give the exact answer in simplest form.
miles

Explanation:

Step1: Write the formula for the area of a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(A\) is the area and \(r\) is the radius.

Step2: Substitute the given area into the formula

Given \(A = 4\pi\), substitute into \(A=\pi r^{2}\):
\(4\pi=\pi r^{2}\)

Step3: Solve for \(r^{2}\)

Divide both sides of the equation \(4\pi=\pi r^{2}\) by \(\pi\):
\(\frac{4\pi}{\pi}=\frac{\pi r^{2}}{\pi}\)
\(4 = r^{2}\)

Step4: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius cannot be negative), \(r=\sqrt{4}\)
\(r = 2\)

Answer:

\(2\)