D. 432π cm^3
First, we need to find the radius of the sphere, which is half of the diameter, so the radius is 6 cm. The volume of the sphere is (4/3)πr^3 = (4/3)π6^3 = 288π cm^3.
The sphere is enclosed by the cylinder, so they share the same radius. The volume of a cylinder is given by πr^2h, where r is the radius and h is the height. Since the height of the cylinder will be equal to the diameter of the sphere, h = 12 cm.
V_cylinder = π * 6^2 * 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?
Responses
A 36π 36π cm ^3
B 72π 72π cm ^3
C 216π 216π cm ^3
D 432π cm ^3
1 answer