Question

the area of a circle is 100π square kilometers. what is the circumference? a = 100π km² give the exact answer in simplest form. kilometers

Explanation:

Step1: Find the radius

The area formula of a circle is \(A = \pi r^{2}\). Given \(A=100\pi\), then \(\pi r^{2}=100\pi\). Divide both sides by \(\pi\): \(r^{2} = 100\). Take the square root of both sides: \(r=\sqrt{100}=10\) (radius \(r>0\)).

Step2: Calculate the circumference

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

Answer:

\(20\pi\) kilometers