Answer:
[tex]h = \frac{V}{\pi r^{2}}[/tex]
h = 4 cm
Step-by-step explanation:
Given the formula for the volume (V) of a cylinder: V = πr ²h, and the following values for volume and radius:
V = 36π cm³
r = 3 cm
First, solve for h:
V = πr ²h
Divide both sides by πr ²:
[tex]\frac{V}{\pi r^{2} } = \frac{\pi r^{2}h}{\pi r^{2} }[/tex]
[tex]h = \frac{V}{\pi r^{2}}[/tex]
Next, solve for the height of the cylinder by substituting the given values for volume and radius into the formula:
[tex]h = \frac{V}{\pi r^{2}}[/tex]
[tex]h = \frac{36\pi }{\pi (3^{2})}[/tex] → π cancels out.
[tex]h = \frac{36}{9}[/tex]
h = 4 cm
