Solve the formula [tex]S = 4 \pi r^2[/tex] for [tex]r[/tex].

A. [tex]r = \sqrt{(S - 4 \pi)}[/tex]

B. [tex]r = \sqrt{\frac{4 \pi}{S}}[/tex]

C. [tex]r = \sqrt{S(4 \pi)}[/tex]

D. [tex]r = \sqrt{\frac{S}{4 \pi}}[/tex]



Answer :

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]