Question

Use the image to answer the 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

18 in.3

27 in.3

36 in.3

40 in.3

Answer 1

Cylinder volume = πr^2h = 54. Cone volume = (1/3)πr^2h = 1/3·54 = 18. Remaining = 54 − 18 = 36 in^3.

Answer: 36 in.^3