Question

the circumference of a circle is 4π meters. what is the area?
give the exact answer in simplest form.
square meters

Explanation:

Step1: Find the radius from the circumference formula

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=4\pi\), we substitute into the formula:
\(4\pi=2\pi r\). Divide both sides by \(2\pi\): \(r = \frac{4\pi}{2\pi}=2\) meters.

Step2: Calculate the area using the radius

The formula for the area of a circle is \(A=\pi r^{2}\). Substitute \(r = 2\) into the formula: \(A=\pi\times(2)^{2}=\pi\times4 = 4\pi\) square meters.

Answer:

\(4\pi\)