Question

the circumference of a circle is 12π inches. what is the area? c = 12π in give the exact answer in simplest form. square inches

Explanation:

Step1: Find the radius

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=12\pi\), we set up the equation \(12\pi=2\pi r\). Dividing both sides by \(2\pi\), we get \(r = \frac{12\pi}{2\pi}=6\) inches.

Step2: Calculate the area

The formula for the area of a circle is \(A=\pi r^{2}\). Substituting \(r = 6\) into the formula, we have \(A=\pi\times6^{2}=\pi\times36 = 36\pi\) square inches.

Answer:

\(36\pi\)