Question

the area of circle z is ( 64pi \text{ ft}^2 ). what is the value of ( r )? ( r = sqrt{\frac{\text{area}}{pi}} ) options: ( r = 4 \text{ ft} ), ( r = 8 \text{ ft} ), ( r = 16 \text{ ft} ), ( r = 32 \text{ ft} )

Explanation:

Step1: Identify the formula and given values

The formula for the radius \( r \) of a circle is \( r = \sqrt{\frac{\text{Area}}{\pi}} \), and the area of the circle is \( 64\pi \, \text{ft}^2 \).

Step2: Substitute the area into the formula

Substitute \( \text{Area} = 64\pi \) into the formula:
\[
r = \sqrt{\frac{64\pi}{\pi}}
\]

Step3: Simplify the expression

Simplify \( \frac{64\pi}{\pi} \) (the \( \pi \) terms cancel out):
\[
r = \sqrt{64}
\]

Step4: Calculate the square root

The square root of 64 is 8:
\[
r = 8
\]

Answer:

\( r = 8 \, \text{ft} \) (corresponding to the option \( r = 8 \, \text{ft} \))