To solve the formula [tex]\( S = 4 \pi r^2 \)[/tex] for [tex]\( r \)[/tex], follow these steps:
1. Start with the original formula:
[tex]\[
S = 4 \pi r^2
\][/tex]
2. Isolate [tex]\( r^2 \)[/tex]:
To isolate [tex]\( r^2 \)[/tex], divide both sides of the equation by [tex]\( 4 \pi \)[/tex]:
[tex]\[
\frac{S}{4 \pi} = r^2
\][/tex]
3. Solve for [tex]\( r \)[/tex]:
To find [tex]\( r \)[/tex], take the square root of both sides:
[tex]\[
r = \sqrt{\frac{S}{4 \pi}}
\][/tex]
Thus, the correct solution for [tex]\( r \)[/tex] is:
[tex]\[
r = \sqrt{\frac{S}{4 \pi}}
\][/tex]
Among the given options, this corresponds to option D:
[tex]\[
\boxed{r = \sqrt{\frac{S}{4 \pi}}}
\][/tex]
