Respuesta :
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]
