Question

the area of a circle is 25π square feet. what is the radius? give the exact answer in simplest form. feet

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 \( A = 25\pi \), we substitute into \( A=\pi r^{2} \):
\( 25\pi=\pi r^{2} \)

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

Divide both sides of the equation \( 25\pi=\pi r^{2} \) by \( \pi \):
\( \frac{25\pi}{\pi}=\frac{\pi r^{2}}{\pi} \), which simplifies to \( 25 = r^{2} \).

Step4: Solve for \( r \)

Take the square root of both sides. Since \( r>0 \) (radius is a non - negative quantity), \( r=\sqrt{25} \).

Answer:

\( 5 \)