1. The formula for the volume of a cone isV =2h.where r is the radius of the base and h is the height of the cone.Part A: Solve the formula for r.

Answer:[tex]r=\sqrt{\frac{3V}{\pi\ h}}[/tex]Step-by-step explanation:The volume of cone is given by:[tex]V=\frac{1}{3}\pi\ r^2\ h[/tex]where [tex]r[/tex] is the radius of the base and [tex]h[/tex] is the height of the cone.We need to solve for [tex]r[/tex]we have [tex]V=\frac{1}{3}\ \pi\ r^2\ h[/tex]Multiplying both sides by 3 to remove [tex]\frac{1}{3}[/tex]⇒ [tex]3\times V=3\times \frac{1}{3}\ \pi\ r^2\ h[/tex]⇒ [tex]3V=\pi\ r^2\ h[/tex]dividing both sides by [tex]\pi\ h[/tex]⇒ [tex]\frac{3V}{\pi\ h}=\frac{\pi r^2 h}{\pi\ h}[/tex]⇒ [tex]\frac{3V}{\pi\ h}=r^2[/tex]Taking square root both sides:⇒ [tex]\sqrt{\frac{3V}{\pi\ h}}=\sqrt{r^2}[/tex]⇒ [tex]\sqrt{\frac{3V}{\pi\ h}}=r[/tex]∴ [tex]r=\sqrt{\frac{3V}{\pi\ h}}[/tex]