Question

solve the formula for the indicated variable. area of a circle: $a = pi r^{2}$; solve for $r$. $r=sqrt{\frac{pi}{a}}$ $r=sqrt{\frac{a}{pi}}$ $r = sqrt{pi a}$ $r=pi a^{2}$

Explanation:

Step1: Isolate $r^{2}$

Divide both sides of $A = \pi r^{2}$ by $\pi$. We get $\frac{A}{\pi}=r^{2}$.

Step2: Solve for $r$

Take the square - root of both sides. Since $r$ represents the radius of a circle (a non - negative quantity in a geometric context), $r=\sqrt{\frac{A}{\pi}}$.

Answer:

$r = \sqrt{\frac{A}{\pi}}$