The cylinder and the cone share a common base and height.

The cylinder and the cone share a common base and height. Calculate the volume of the cylinder if the volume of the cone is 12.

The volume of the cylinder Vc is determined by the formula Vc = S * H, where S is the area of the base of the cylinder, H is the height of the cylinder. The volume of the cone Vk is determined by the formula Vk = 1/3 * S * H, where S is the area of the base of the cone, H is the height of the cone. Let us express the height of the cone H = 3 * Vк / S. Now we will substitute its value in the formula for the volume of the cylinder Vc = S * 3 * Vk / S = 3 * Vk. Vts = 3 * 12 = 36. We see that the volume of a cylinder with the same base and height is 3 times the volume of the cone.
Answer: Cylinder volume 36