A sculptor created a design by carving a cone out of a cylinder the cone and cylinder share the same height and radius the volume of the cylinder before removing the cone is 54 in cubed what is the volume of the amount remaining
Let's assume the height and radius of both the cone and the cylinder are h and r, respectively.
The volume of the cylinder is given by Vcylinder = πr^2h.
We are told that Vcylinder = 54 in^3.
The volume of the cone is given by Vcone = (1/3)πr^2h.
Since the cone and cylinder have the same height and radius, we can express their volumes in terms of Vcylinder: Vcone = (1/3) Vcylinder.
To find the remaining volume, we subtract the volume of the cone from the volume of the cylinder: Vremaining = Vcylinder - Vcone.
Substituting the expressions for Vcylinder and Vcone into the equation:
Vremaining = 54 in^3 - (1/3) × 54 in^3
= 54 in^3 - 18 in^3
= 36 in^3.
Therefore, the volume of the remaining amount is 36 in^3.