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 54in .^ 3 what is the volume of the amount remaining? (1 point)
18 ln.^ 2
O 27 ln.^ 3
30 ln^ 3
40 ln.^ 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, we can let the radius be r and the height be h.
The volume of the cylinder before removing the cone is given as 54in^3. Therefore, we have:
54 = πr^2h ----(1)
Now, the volume of a cone is given by the formula V = (1/3)πr^2h. Since the cone is carved out of the cylinder, the remaining volume is the volume of the cylinder minus the volume of the cone. Therefore, the volume of the remaining part is:
V remaining = 54 - (1/3)πr^2h
We can simplify this expression by substituting the value of πr^2h from equation (1):
V remaining = 54 - (1/3)(54)
V remaining = 54 - 18
V remaining = 36
So the volume of the remaining part is 36in^3.
Answer: The volume of the amount remaining is 36in^3.