Question

The formula for the volume V of a cylinder is LaTeX: V=\pi r^2hV = π r 2 h, where r is the radius of the base and h is the height of the cylinder. Select the formula for h. Then select the height of a cylinder with a volume of LaTeX: 36\pi36 π cm3 and a base with a radius of 3 cm.

Answer 1

`h = 4 cm`

Explanation:

Volume of cylinder is given as
`V = \pi r^2h`,

r = radius of base of cylinder, h = height of the cylinder.

Let's make h (height) the subject of the formula (i.e. select the formula for h).

`V = \pi r^2h`

Divide both sides by πr²

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

`(V)/(\pi r^2) = h` (πr² crosses out πr²)

Rewrite the formula:

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

Given a cylinder of Volume (V) = 36π cm³, and radius (r) = 3 cm,

height of the cylinder can be selected by plugging these values into the formula for h (height) we selected above. Thus:

`h = (36 \pi)/(\pi 3^2)`

Simplify:

`h = (36 \pi)/(\pi * 9)`

`h = (36)/(9)` (π crosses out π)

`h = 4 cm`