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
27 in.3
27 in. cubed
40 in.3
40 in. cubed
36 in.3
36 in. cubed
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The volume of the cylinder before removing the cone is 54 in.^3. Since the cone is removed from the cylinder, the volume of the remaining material will be the volume of the cylinder minus the volume of the cone.
The volume of a cone is given by V = (1/3)πr^2h, where r is the radius and h is the height.
Since the cone and cylinder have the same radius and height, the volume of the cone is (1/3)πr^2h = (1/3)πr^2h = 1/3 of the volume of the cylinder.
Therefore, the volume of the remaining material is:
54 in.^3 - (1/3) * 54 in.^3 = 36 in.^3
Therefore, the correct answer is:
36 in.^3