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?
36 in.336 in. cubed27 in.327 in. cubed40 in.340 in. cubed18 in.3
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Since the cone and cylinder share the same radius and height, the volume of the removed cone is equal to 1/3 times the volume of the cylinder.
The volume of the cone is given by the formula V = (1/3)πr^2h.
The volume of the remaining amount is equal to the volume of the cylinder minus the volume of the removed cone.
Given that the volume of the cylinder before removing the cone is 54 in.3, we can set up the following equation:
54 = πr^2h
We are asked to find the volume of the remaining amount, which is equal to the volume of the cylinder minus the volume of the cone. Let's call the volume of the remaining amount V_remaining.
V_remaining = (πr^2h) - (1/3)πr^2h = (2/3)πr^2h
To solve for V_remaining, we need to know the values of r and h.
Since we do not have enough information to determine the values of r and h, we cannot calculate the exact volume of the remaining amount. Therefore, none of the given answer choices (36 in.3, 36 in.3, 27 in.3, 27 in.3, 40 in.3, 40 in.3, 18 in.3, 18 in.3) are correct.