Final answer:
The volume of the cylinder inscribed within a sphere with a diameter of 30 units and a height of 20 units is calculated as 6000π cubic units. Since none of the provided multiple choice options match this result, there may be a mistake in the question. The calculation used the formula V = πr²h.
Step-by-step explanation:
To find the volume of the cylinder inscribed within a sphere with a diameter of 30 units, we first need to determine the radius of the cylinder. Since the diameter of the sphere is equal to 30, the radius of the sphere (and thus the cylinder) is 15 units. The height of the cylinder is given as 20 units. The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Using these measurements:
V = π(15²)(20)
V = 300π(20)
V = 6000π cubic units
However, as there are no matching answers from A to D, there might be a typo or a misinterpretation of the question. None of the given options A. 9420π, B. 14,130π, C. 15,700π, or D. 21,200π cubic units matches the calculated volume of 6000π cubic units.