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
36 in.^3
18 in^3
27 in^3
40 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 the cylinder share the same radius and height, the volume of the cone can be calculated as one-third of the volume of the cylinder: V_cone = (1/3) * V_cylinder.
If the volume of the cylinder before removing the cone is 54 in^3, then V_cylinder = 54 in^3.
Substituting this value into the formula for the volume of the cone: V_cone = (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 36 in^3.