Question

The formula for the volume of a cone is V=1/3πr^2h Solve the formula for the radius r.

Answer 1

Answer:

$r = \sqrt{ \frac{3V}{\pi h}}$

Step-by-step explanation:

$V = \frac{1}{3} \pi {r}^{2} h$

First multiply through by 3 to eliminate the fraction

That's

$3V = 3 \times \frac{1}{3} \pi {r}^{2} h \\ 3V = \pi {r}^{2} h$

Divide both sides by πh

That's

$\frac{3V}{\pi h} = \frac{\pi {r}^{2}h }{\pi h} \\ {r}^{2} = \frac{3V}{\pi h}$

Find the square root of both sides to make r stand alone

We have

$\sqrt{ {r}^{2} } = \sqrt{ \frac{3V}{\pi h}}$

We have the final answer as

$r = \sqrt{ \frac{3V}{\pi h}}$

Hope this helps you