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.
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
1 answer