Question

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.) 40 in.^3
B.) 36 in.^3
C.) 18 in.^3
D.) 27 in. ^3

Answer 1

[AI-generated answer — Bot GPT 3.5]

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 has the same radius and height as the cylinder, the volume of the cone removed is given by the formula V_cone = (1/3)πr^2h.

Given that the volume of the cylinder is 54 in.^3, we have V_cylinder = πr^2h = 54 in.^3.

Substitute V_cylinder into the formula for the volume of the cone:

V_cone = (1/3)πr^2h = (1/3) * 54 = 18 in.^3.

Therefore, the volume of the amount remaining after removing the cone is 54 - 18 = 36 in.^3.

The correct answer is B.) 36 in.^3.