A sculptor created a design by carving a cone out of a cylinder. The cone and
cylinder share the same radius and height. If the volume of the cylinder before
removing the cone is 54 in.³, what is the volume of the amount remaining?
(1 point)
The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height.
Given that the volume of the cylinder is 54 in.³, we can plug in the values and solve for the radius and height:
54 = πr²h
Since the cone that is carved out of the cylinder is the same height and radius as the cylinder, the volume of the cone is 1/3 of the volume of the cylinder:
V_cone = 1/3 * V_cylinder
V_cone = 1/3 * 54
V_cone = 18 in.³
The volume remaining after carving out the cone is the volume of the cylinder minus the volume of the cone:
V_remaining = V_cylinder - V_cone
V_remaining = 54 - 18
V_remaining = 36 in.³
Therefore, the volume of the amount remaining is 36 in.³.