Final answer:
The volume of the cylinder inscribed within a sphere of diameter 30 units is 4500π cubic units, calculated using the formula V = πr²h, with r being half of the sphere's diameter and h being the height of the cylinder.
Step-by-step explanation:
To find the volume of the cylinder that is inscribed within a sphere with a diameter of 30 units, we need to use the formula for the volume of a cylinder, which is V = πr²h. Since the cylinder is inscribed in a sphere, its diameter will be equal to the diameter of the sphere, which is 30 units. Therefore, the radius r of the cylinder will be half of the diameter, so r = 15 units. Given that the height h of the cylinder is 20 units, we can plug these values into the formula.
The calculation is as follows:
• V = πr²h
• V = π(15²)(20)
• V = 225³20π
• V = 4500π
• Therefore, the volume of the cylinder is 4500π cubic units.
However, none of the options given (a-d) match the correct volume calculated. The volume of the cylinder is 4500π cubic units, which is not listed in the given choices. There is either a mistake in the provided choices, or the question might be missing some information or context.