Question

To find the volume of a cone, we use the formula V= 13r2h, where V is the volume, r is the radius of the circle of the base, and h is the height of the cone. Rewrite the equation so that the positive value of r is written in terms of V and h. I need help with this problem.

Answer 1

`r = \sqrt{(3V)/(\pi h)}`

Explanation:

Given

`V = (1)/(3)\pi r^2h`

Required

Solve for r

`V = (1)/(3)\pi r^2h`

Multiply both sides by 3

`3 * V = (1)/(3)\pi r^2h * 3`

`3 V = \pi r^2h`

Divide both sides by
`\pi h`

`(3V)/(\pi h) = (\pi r^2h)/(\pi h)`

`(3V)/(\pi h) = r^2`

Take square root of both sides

`\sqrt{(3V)/(\pi h)} = √(r^2)`

`\sqrt{(3V)/(\pi h)} = r`

`r = \sqrt{(3V)/(\pi h)}`