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
40 in.3
40 in. cubed
36 in.3
36 in. cubed
27 in.3
27 in. cubed
18 in.3
18 in. cubed
The volume of the amount remaining can be calculated by subtracting the volume of the cone from the volume of the cylinder.
Since the cone and cylinder have the same height and radius, the volume of the cylinder is given by the formula:
Volume of cylinder = π × r^2 × h
Given that the volume of the cylinder is 54 in.3, we can say:
54 = π × r^2 × h
To find the volume of the cone, we can use the formula:
Volume of cone = (1/3) × π × r^2 × h
Since the cone has the same radius and height as the cylinder, we can substitute the values:
Volume of cone = (1/3) × π × r^2 × h = (1/3) × 54 = 18 in.3
Therefore, the volume of the amount remaining is:
Volume remaining = 54 - 18 = 36 in.3
So the correct answer is:
36 in.3