Question

the circumference of a circle is 20π inches. what is the area? give the exact answer in simplest form. square inches

Explanation:

Step1: Find the radius using the circumference formula

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=20\pi\), we substitute into the formula:
\(20\pi=2\pi r\).
Divide both sides by \(2\pi\): \(r = \frac{20\pi}{2\pi}=10\) inches.

Step2: Calculate the area using the radius

The formula for the area of a circle is \(A=\pi r^{2}\). Substitute \(r = 10\) into the formula:
\(A=\pi\times(10)^{2}=\pi\times100 = 100\pi\) square inches.

Answer:

\(100\pi\)