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)
The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height. The volume of a cylinder is given by the formula V = πr^2h.
Since the cone and cylinder have the same radius and height, we can set up the following equation:
54 = πr^2h + (1/3)πr^2h
Combining like terms, we get:
54 = (4/3)πr^2h
To find the volume of the remaining amount after removing the cone, we need to subtract the volume of the cone from the volume of the cylinder:
Volume remaining = Volume of cylinder - Volume of cone
Volume remaining = πr^2h - (1/3)πr^2h
Plugging in the values we know:
Volume remaining = 54 - (1/3) * 54
Volume remaining = 54 - 18
Volume remaining = 36 in.^3
Therefore, the volume of the amount remaining is 36 in.^3.