Question

the area of a circle is 16π square centimeters. what is the radius? a = 16π cm² give the exact answer in simplest form. centimeters

Explanation:

Step1: Write the formula for the area of a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(A\) is the area and \(r\) is the radius.

Step2: Substitute the given area into the formula

Given \(A = 16\pi\), we substitute into the formula: \(16\pi=\pi r^{2}\).

Step3: Solve for \(r^{2}\)

Divide both sides of the equation \(16\pi=\pi r^{2}\) by \(\pi\). We get \(r^{2}=\frac{16\pi}{\pi}=16\).

Step4: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius is a non - negative quantity), \(r = \sqrt{16}=4\).

Answer:

\(4\)