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)
18 in.3
18 in. cubed
27 in.3
27 in. cubed
40 in.3
40 in. cubed
36 in.3
The volume of the cylinder before removing the cone is given as 54 in³. Since the cone and cylinder have the same radius and height, the volume of the cone that is carved out is equal to 1/3 of the volume of the cylinder (as the volume of a cone is given by the formula V = (1/3)πr²h).
Therefore, the volume of the cone carved out is (1/3) * 54 = 18 in³.
The volume of the remaining amount is thus equal to the volume of the cylinder minus the volume of the carved out cone.
Volume of remaining amount = 54 in³ - 18 in³ = 36 in³.
Therefore, the volume of the amount remaining is 36 in³.