Answer:
[tex]r=\sqrt{\dfrac{3V}{\pi h}}[/tex]
Step-by-step explanation:
Given equation:
[tex]V=\dfrac{1}{3} \times \pi r^2 h[/tex]
To isolate [tex]r[/tex], multiply both sides by 3:
[tex]\implies V \times 3=\dfrac{1}{3} \times \pi r^2 h \times 3[/tex]
[tex]\implies 3V= \pi r^2 h[/tex]
Divide both sides by [tex]\pi h[/tex]:
[tex]\implies \dfrac{3V}{\pi h}= \dfrac{\pi r^2 h}{\pi h}[/tex]
[tex]\implies \dfrac{3V}{\pi h}=r^2[/tex]
Square root both sides:
[tex]\implies \sqrt{r^2}=\sqrt{\dfrac{3V}{\pi h}}[/tex]
As the radius is positive only:
[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0[/tex]
[tex]\implies r=\sqrt{\dfrac{3V}{\pi h}}[/tex]
