Question

the area of circle z is 64π ft². what is the value of r? r = 4 ft r = 8 ft r = 16 ft r = 32 ft r = √(area/π)

Explanation:

Step1: Recall area formula

The area formula of a circle is $A = \pi r^{2}$. Given $A = 64\pi$, we can solve for $r$.

Step2: Rearrange formula

From $A=\pi r^{2}$, we get $r^{2}=\frac{A}{\pi}$. Substituting $A = 64\pi$, we have $r^{2}=\frac{64\pi}{\pi}=64$.

Step3: Solve for r

Taking the square - root of both sides, $r=\sqrt{64}=8$ (we consider the positive value since $r$ represents the radius of a circle).

Answer:

$r = 8$ ft