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) Responses 40 in.3 40 in. cubed 18 in.3 18 in. cubed 36 in.3 36 in. cubed 27 in.3
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Since the cone and cylinder share the same radius and height, the volume of the cone is exactly one-third of the volume of the cylinder.
Given that the volume of the cylinder before removing the cone is 54 in.3, the volume of the cone is 1/3 * 54 in.3 = 18 in.3.
Therefore, the volume of the amount remaining is the volume of the cylinder (54 in.3) minus the volume of the cone (18 in.3).
Volume remaining = 54 in.3 - 18 in.3 = 36 in.3
So, the correct answer is 36 in.3.