Question

A cone has a volume of 8 pi cubic inches what is the radius of the cone?

Answer 1

`r = \sqrt{(24)/(h)}` inches

Explanation:

Volume of a cone =
`(1)/(3) \pi r^(3)h`

where: r = radius of cone

h = perpendicular height of the cone

Provided volume of cone = 8π cubic inches

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

Cross multiplication is applied and 'r' is isolated:

`3(8\pi ) = \pi r^(2) h`

`24\pi =\pi r^(2) h`

`r^(2) h = (24\pi)/(\pi)`

`\pi` in the numerator and denominator cancel each other out completely:

`r^(2) h = 24`

`r^(2) = (24)/(h)`

Taking the square root on both sides of the equation in order to get rid of the square:

`r = \sqrt{(24)/(h)}` inches