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)
O 40 in.3
○ 27 in.³
○ 36 in.3
○ 18 in.3
First, let's find the volume of the cone that was carved out. The volume of a cone is given by V = (1/3)πr^2h, where r is the radius and h is the height.
Given that the cone and cylinder share the same radius and height, the volume of the cylinder before removing the cone is equal to the volume of the cylinder after removing the cone plus the volume of the cone.
Volume of cylinder = 54 in.³
Volume of cone = (1/3)πr^2h
Volume of cylinder = Volume of cylinder after removing cone + Volume of cone
54 = Volume of cylinder after removing cone + (1/3)πr^2h
Since the radius and height of the cone and cylinder are the same, the height of the cone is equal to the height of the cylinder.
54 = Volume of cylinder after removing cone + (1/3)πr^2h
54 = Volume of cylinder after removing cone + Volume of cylinder
54 = Volume of cylinder after removing cone + 54
Volume of cylinder after removing cone = 0 in.³
Therefore, the volume of the amount remaining is 0 in.³.