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?
a. 36 in.3
b. 40 in.3
c. 18 in.3
d. 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.
The volume of the cone is given by the formula V = (1/3)πr^2h.
Since the cone and the cylinder have the same radius and height, the volume of the cone is (1/3) of the volume of the cylinder.
So, the volume of the cone is (1/3) * 54 in.3 = 18 in.3.
Therefore, the volume of the amount remaining is 54 in.3 - 18 in.3 = 36 in.3.
The correct answer is a. 36 in.3.