A sculptor created a design by carving a cone out of a cylinder the cone and the cylinder share the same radius and height if the volume of the cylinder before removing the cone is 54 in cubed what is the volume of the amount remaining
The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height. Since the cylinder and the cone share the same radius and height, we can say that the volume of the cone is 1/3 times the volume of the cylinder.
Let's denote the radius and height of the cylinder as r and h, respectively.
The volume of the cylinder is given as 54 in^3, so we have:
54 = πr^2h
Since the cone has 1/3 of the volume of the cylinder, we can express the volume of the cone as 1/3 times the volume of the cylinder:
V_cone = (1/3) * πr^2h
Substituting the value of the volume of the cylinder, we get:
V_cone = (1/3) * 54 = 18 in^3
Since we want to find the volume of the amount remaining, we need to subtract the volume of the cone from the volume of the cylinder:
Volume remaining = Volume of cylinder - Volume of cone
= 54 - 18
= 36 in^3
Therefore, the volume of the remaining amount is 36 in^3.