Question

a. if a circle has a circumference of 12π cm, what is its area?
b. if a circle of radius r and a square with a side of length b have equal areas, express r in terms of b.
a. the area of the circle is
(simplify your answer, including pe an exact answer, using π as needed )

Explanation:

Step1: Find the radius of the circle

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=12\pi\), we have \(12\pi=2\pi r\). Dividing both sides by \(2\pi\), we get \(r = 6\) cm.

Step2: Calculate the area of the circle

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

Answer:

\(36\pi\)