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
18 in. cubed
40 in.3
40 in. cubed
36 in.3
36 in. cubed
27 in.3
The volume of the amount remaining can be calculated by subtracting the volume of the cone from the volume of the cylinder.
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 of the cone.
Since the cone and cylinder have the same radius and height, the volume of the cone is also 1/3 times the volume of the cylinder. Therefore, the volume of the remaining amount is 2/3 times the volume of the cylinder.
Given that the volume of the cylinder is 54 in^3, the volume of the remaining amount is (2/3) * 54 = 36 in^3.
Therefore, the answer is 36 in.3 or 36 in. cubed.