Question

a circle has an area of 16π square centimeters. what is the length of its radius? 4 of 5 questions 256 cm 4 cm 32 cm 8 cm

Explanation:

Step1: Recall 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 \(A=\pi r^{2}\):
\(16\pi=\pi r^{2}\)

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

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

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:

B. \(4\) cm