Question

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

40 in.3
40 in. cubed

27 in.3
27 in. cubed

36 in.3
36 in. cubed

18 in.3

Answer 1

The volume of the remaining amount can be found by subtracting the volume of the cone from the volume of the cylinder.

Since the cone and cylinder have the same radius and height, they are similar shapes. The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.

The volume of the cone is therefore (1/3)πr^2h.

The volume of the cylinder is given as 54 in.3.

To find the volume of the remaining amount, we subtract the volume of the cone from the volume of the cylinder: 54 - (1/3)πr^2h.

Since no specific values for r and h are given in the question or image, we cannot determine the exact volume of the remaining amount. Therefore, none of the given options (40 in.3, 27 in.3, 36 in.3, 18 in.3) can be the correct answer.