Answer:
[tex] h = 4 cm [/tex]
Step-by-step explanation:
Volume of cylinder is given as [tex] V = \pi r^2h [/tex],
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).
[tex] V = \pi r^2h [/tex]
Divide both sides by πr²
[tex] \frac{V}{\pi r^2} = \frac{\pi r^2h}{\pi r^2} [/tex]
[tex] \frac{V}{\pi r^2} = h [/tex] (πr² crosses out πr²)
Rewrite the formula:
[tex] h = \frac{V}{\pi r^2} [/tex]
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:
[tex] h = \frac{36 \pi}{\pi 3^2} [/tex]
Simplify:
[tex] h = \frac{36 \pi}{\pi * 9} [/tex]
[tex] h = \frac{36}{9} [/tex] (π crosses out π)
[tex] h = 4 cm [/tex]
