Question

the area of a circle is 16π square meters. what is the diameter?
a = 16π m²
give the exact answer in simplest form.
meters

Explanation:

Step1: Recall the area formula of a circle

The area formula of a circle is \(A = \pi r^{2}\), where \(A\) is the area and \(r\) is the radius. Given \(A = 16\pi\), we have \(\pi r^{2}=16\pi\).

Step2: Solve for the radius \(r\)

Divide both sides of the equation \(\pi r^{2}=16\pi\) by \(\pi\): \(r^{2}=\frac{16\pi}{\pi}=16\). Then take the square - root of both sides: \(r = \sqrt{16}=4\) (we take the positive value since \(r>0\) for a radius).

Step3: Calculate the diameter \(d\)

The diameter \(d\) of a circle is related to the radius by \(d = 2r\). Substitute \(r = 4\) into the formula: \(d=2\times4 = 8\).

Answer:

\(8\)