Question

A cone is placed inside a cylinder. The apex of the cone touching the center of the top circle of the cylinder is highlighted with a dot. The cone with its base is drawn in dashed lines. The base of the cone is common with the base of the cylinder.

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

27 in.3

27 in. cubed

18 in.3

18 in. cubed

36 in.3

36 in. cubed

40 in.3

Answer 1

Cylinder volume = base area × height = 54 in³. Cone (same base and height) has volume = 1/3 × cylinder = 1/3·54 = 18 in³.
Remaining = 54 − 18 = 36 in³.

Answer: 36 in³.