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 has the same radius and height as the cylinder, the volume of the cone removed is given by the formula V_cone = (1/3)πr^2h.
Given that the volume of the cylinder is 54 in.^3, we have V_cylinder = πr^2h = 54 in.^3.
Substitute V_cylinder into the formula for the volume of the cone:
V_cone = (1/3)πr^2h = (1/3) * 54 = 18 in.^3.
Therefore, the volume of the amount remaining after removing the cone is 54 - 18 = 36 in.^3.
The correct answer is B.) 36 in.^3.
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.) 40 in.^3
B.) 36 in.^3
C.) 18 in.^3
D.) 27 in. ^3
1 answer