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?(1 point)
Responses
40 in.3
40 in. cubed
36 in.3
36 in. cubed
27 in.3
27 in. cubed
18 in.3
To find the volume of the material remaining after carving the cone out of the cylinder, we first find the volume of the cone and then subtract it from the volume of the cylinder. Since the cone and cylinder share the same radius (r) and height (h), we can use their respective volume formulas:
Volume of cylinder (V_cylinder) = πr^2h
Volume of cone (V_cone) = (1/3)πr^2h
Given that the volume of the cylinder before removing the cone is 54 cubic inches, we have:
V_cylinder = 54 in³
We can find the volume of the cone by using the fact that the cone has a volume that is 1/3 that of a cylinder with the same radius and height:
V_cone = (1/3)V_cylinder
V_cone = (1/3) * 54 in³
V_cone = 18 in³
Now, we subtract the volume of the cone from the volume of the cylinder to find the volume of the material remaining:
Volume remaining = V_cylinder - V_cone
Volume remaining = 54 in³ - 18 in³
Volume remaining = 36 in³
Therefore, the volume of the amount remaining after carving the cone out of the cylinder is 36 cubic inches. The correct answer is:
36 in.3
36 in. cubed