Question

the circumference of a circle is 14π cm. what is the area, in square centimeters? express your answer in terms of π.

Explanation:

Step1: Find the radius of the circle

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=14\pi\), we have \(14\pi=2\pi r\).
Divide both sides by \(2\pi\): \(r=\frac{14\pi}{2\pi}=7\) cm.

Step2: Calculate the area of the circle

The formula for the area of a circle is \(A=\pi r^{2}\). Substitute \(r = 7\) into the formula: \(A=\pi\times(7)^{2}\).
Simplify: \(A = 49\pi\) \(cm^{2}\).

Answer:

\(49\pi\) square centimeters.