Final answer:
The formula for the cylinder's height is h = V / (πr²). Using the volume of 36π cm³ and the radius of 3 cm, the height is calculated to be 4 cm.
Step-by-step explanation:
To solve the formula V = πr²h for the height h, we rearrange the formula so that h is on one side of the equation. To do this, we divide both sides by πr², which gives us h = V / (πr²). Now we can find the height of a cylinder when we're given its volume and the radius of its base.
Using the provided information, where V is 36π cm³ and the radius r is 3 cm, we plug these values into the rearranged formula:
h = 36π cm³ / (π × 3² cm²).
After simplifying, we're left with:
h = 36π cm³ / (9π cm²)
h = 4 cm
Therefore, the height of the cylinder is 4 cm.