Since the sphere is enclosed by the cylinder, the diameter of the sphere is equal to the height of the cylinder. Therefore, the height of the cylinder is 12 cm.
The radius of the sphere is half of its diameter, so the radius of the sphere is 6 cm.
The radius of the cylinder is also 6 cm.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Substituting the values, we get V = π(6^2)(12) = π(36)(12) = 432π cm^3.
Therefore, the volume of the cylinder is 432π cm^3.
Consider the sphere enclosed by the cylinder. If the diameter of the sphere is 12 cm, what is the volume of the cylinder?
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