Final answer:
To find the height of a right cone with a volume of 4125π cubic units and a diameter of 30 units, divide the provided volume by one-third of pi times the square of the radius (15 units). The height of the cone is 55 units.
Step-by-step explanation:
The volume of a right cone is given by the formula V = ⅓πr²h, where V is the volume, r is the radius, and h is the height. Since the volume of the cone is provided as 4125π cubic units and the diameter is 30 units, we first determine the radius of the cone, which is half the diameter, so r = 15 units. Plugging these values into the volume formula and solving for the height h, we get:
V = ⅓πr²h
4125π = ⅓π(15²)h
4125π = ⅓π(225)h
Divide both sides by ⅓π(225) to find the height:
h = 4125π / (⅓π(225))
h = 55
Therefore, the height of the cone is 55 units.