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
27 in.3
27 in. cubed
36 in.3
The volume of the cone is equal to one-third the volume of the cylinder. Since the volume of the cylinder before removing the cone is given as 54 in^3, the volume of the cone is 1/3 * 54 in^3 = 18 in^3.
Therefore, the volume of the remaining amount after removing the cone would be the volume of the cylinder minus the volume of the cone.
Remaining volume = Volume of cylinder - Volume of cone
= 54 in^3 - 18 in^3
= 36 in^3
So, the volume of the amount remaining is 36 in^3.