The volume of a cylinder is given by V = πr^2h, where r is the radius and h is the height. Since the cone and cylinder have the same radius and height, we can denote them as r and h respectively.
Given that the initial volume of the cylinder is 54 in^3, we have:
54 = πr^2h
Since the cone and cylinder share the same height, the volume of the cone can be calculated as V_cone = (1/3)πr^2h.
The volume of the remaining shape after the cone is removed can be calculated as the volume of the cylinder minus the volume of the cone:
V_remaining = V_cylinder - V_cone
V_remaining = πr^2h - (1/3)πr^2h
V_remaining = (2/3)πr^2h
Substituting h from the initial cylinder volume equation: 54 = πr^2h, we get:
V_remaining = (2/3)πr^2 * (54 / πr^2)
V_remaining = (2/3) * 54
V_remaining = 36 in^3
Therefore, the volume of the remaining shape after removing the cone is 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?
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1 answer