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

Answer:

$h = 4 cm$

Step-by-step 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

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

$\frac{V}{\pi r^2} = h$ (πr² crosses out πr²)

Rewrite the formula:

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

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:

$h = \frac{36 \pi}{\pi 3^2}$

Simplify:

$h = \frac{36 \pi}{\pi * 9}$

$h = \frac{36}{9}$ (π crosses out π)

$h = 4 cm$