Question

a circular pool of water is shrinking as it drains. the diagram shows the shrinkage
a formula for the area, $a$, of the circular pool is given by the equation $a = \pi(r - 3)^2$
which is a formula for $r$
a $r = \sqrt{\frac{a}{\pi}-3}$
b $r = \sqrt{\frac{a}{\pi}} - 3$
c $r = \sqrt{\frac{a}{\pi}} + 3$
d $r = \frac{\sqrt{a}}{\pi} - 3$

Explanation:

Step1: Isolate squared term

Divide both sides by $\pi$:
$\frac{A}{\pi} = (r-3)^2$

Step2: Eliminate square root

Take square root of both sides:
$\sqrt{\frac{A}{\pi}} = r-3$

Step3: Solve for $r$

Add 3 to both sides:
$r = \sqrt{\frac{A}{\pi}} + 3$

Answer:

C. $r = \sqrt{\frac{A}{\pi}} + 3$