Question

the area of a circle is 49π square centimeters. what is the radius?
a = 49π 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 \(A = 49\pi\), we substitute into \(A=\pi r^{2}\):
\(49\pi=\pi r^{2}\)

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

Divide both sides of the equation by \(\pi\):
\(\frac{49\pi}{\pi}=\frac{\pi r^{2}}{\pi}\)
\(49 = r^{2}\)

Step4: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius is a non - negative quantity), \(r=\sqrt{49}\)
\(r = 7\)

Answer:

\(7\)