Answer:
[tex]r = \pm\sqrt{\frac{A}{4 \pi}}[/tex]
Step-by-step explanation:
Given:
The given equation is [tex]A = 4 \pi r^{2}[/tex]
We need to solve the given equation for r.
Rewrite the equation as.
[tex]4 \pi r^{2}=A[/tex]
Divide both side of the equation by 4π and simplify
[tex]\frac{4 \pi r^{2}}{4 \pi}=\frac{A}{4 \pi}[/tex]
[tex]r^{2}=\frac{A}{4 \pi}[/tex]
Take the square root both side of the equation.
[tex]\sqrt{r^{2} } = \sqrt{\frac{A}{4 \pi}}[/tex]
[tex]r = \pm\sqrt{\frac{A}{4 \pi}}[/tex]
Therefore, the solution for r is both positive or negative [tex]r = \pm\sqrt{\frac{A}{4 \pi}}[/tex]
