Question

the area of a circle is 81π in². what is the circumference, in inches? express your answer in terms of π.

Explanation:

Step1: Find the radius of the circle

The formula for the area of a circle is \(A = \pi r^{2}\). Given \(A = 81\pi\), we have \(\pi r^{2}=81\pi\). Divide both sides by \(\pi\): \(r^{2}=81\). Then \(r = 9\) (since radius \(r>0\)).

Step2: Calculate the circumference of the circle

The formula for the circumference of a circle is \(C = 2\pi r\). Substitute \(r = 9\) into the formula: \(C=2\pi\times9 = 18\pi\).

Answer:

\(18\pi\)