Question

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

Explanation:

Step1: Find the radius of the circle

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=20\pi\), we set up the equation \(2\pi r=20\pi\). Dividing both sides by \(2\pi\), we get \(r = \frac{20\pi}{2\pi}=10\) centimeters.

Step2: Calculate the area of the circle

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

Answer:

\(100\pi\)