Question

the circumference of a circle is 5π miles. what is the area? give the exact answer in simplest form. square miles

Explanation:

Step1: Find the radius

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C = 5\pi\), we have \(5\pi=2\pi r\). Dividing both sides by \(2\pi\), we get \(r=\frac{5}{2}\) miles.

Step2: Calculate the area

The formula for the area of a circle is \(A=\pi r^{2}\). Substitute \(r = \frac{5}{2}\) into the formula: \(A=\pi(\frac{5}{2})^{2}=\pi\times\frac{25}{4}=\frac{25\pi}{4}\) square miles.

Answer:

\(\frac{25\pi}{4}\)