Question

the area of a circle is 100π m². what is the circumference, in meters? 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 \(A = 100\pi\), we have \(\pi r^{2}=100\pi\). Divide both sides by \(\pi\): \(r^{2}=100\). Then \(r = 10\) (since \(r>0\)).

Step2: Calculate the circumference of the circle

The formula for the circumference of a circle is \(C = 2\pi r\). Substitute \(r = 10\) into the formula: \(C=2\pi\times10 = 20\pi\).

Answer:

\(20\pi\)