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?
A. 18 in.^3
B. 36 in.^3
C. 40 in.^3
D. 27 in.^3
B. 36 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 cylinder before removing the cone is the same as the volume of the cone.
The volume of a cone is given by the formula V = (1/3)πr^2h.
Since the volume of the cylinder is 54 in.^3, we have:
54 = πr^2h
And the volume of the cone is:
V = (1/3)πr^2h
Substituting the first equation into the second equation, we have:
V = (1/3)*54
V = 18
Therefore, the volume of the amount remaining after carving out the cone from the cylinder is 54 - 18 = 36 in.^3.