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?
(1 point)
• 40 in.3
• 36 in.3
• 18 in.3
• 27 in.
3

Answer 1

Explanation:

the volume of a cylinder is

pi×r²×h

r being the radius, h the height.

the volume of a cone is

pi×r²×h/3

so, when r and h are the same, then the volume of the cylinder is 3 times the volume of the cone.

or the other way around, the volume of the cone is 1/3 of the volume of the cylinder.

volume of the full cylinder = 54 in³.

the volume of the cone is then 54/3 = 18 in³.

when removing the volume of the cone we are left with

54 - 18 = 36 in³