Question

the formula for the surface area of a sphere is $a = 4\pi r^2$. rearrange the formula to solve for $r$, the radius of the circle.\
options:\
$r = \sqrt{\frac{4a}{\pi}}$\
$r = \sqrt{\frac{4\pi}{a}}$\
$r = \sqrt{\frac{\pi}{4a}}$\
$r = \sqrt{\frac{a}{4\pi}}$

Explanation:

Step1: Isolate \( r^{2} \)

Given \( A = 4\pi r^{2} \), divide both sides by \( 4\pi \):
\( \frac{A}{4\pi}=r^{2} \)

Step2: Solve for \( r \)

Take the square - root of both sides. Since \( r>0 \) (radius is non - negative), we have:
\( r = \sqrt{\frac{A}{4\pi}} \)

Answer:

\( r=\sqrt{\frac{A}{4\pi}} \)