Question

The maximum volume (in cu. units) of the cylinder which can be inscribed in a sphere of radius 12 units is:

• A. \( 384 \sqrt{3} \pi \)
• B. \( 768 \sqrt{3} \pi \)
• C. \( 768 \pi / \sqrt{3} \)
• D. \( 1152 \pi / \sqrt{3} \)

Hint:

To maximize the volume of a cylinder inscribed in a sphere, use the relation between radius and height of the sphere, and then differentiate to find the maximum.