Question

the circumference of a circle is 20π in. what is the area, in square inches? express your answer in terms of π.

Explanation:

Step1: Find the radius

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=20\pi\), we have \(2\pi r=20\pi\). Dividing both sides by \(2\pi\), we get \(r = 10\) inches.

Step2: Calculate the area

The formula for the area of a circle is \(A=\pi r^{2}\). Substituting \(r = 10\) into the formula, we have \(A=\pi\times10^{2}=100\pi\) square inches.

Answer:

\(100\pi\) square inches