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Khi thinks that when the flags below are rotated, the (volume of ) (volume of ) (volume of ()).

Decide if he is correct. If he is incorrect, explain the error in his logic. 

Start by visualizing the terms in Khi's equation: What does Volume and Volume look like? What does Volume () look like?

Volume is cone with radius . Volume is a cylinder with radius . Each is a separate 3D solid whose volumes are added together after they are computed: [cone with ] + [cylinder with ]

Try computing the volume of each:
Volume Volume cone cylinder
Volume BigCone − SmallCone
Evaluate and compare.

Volume () is a single 3D solid that looks like a cone with its top cut off. To compute its volume, it must be dissected into pieces:
[large cone with ] [small cone with ]

Use the eTool below to visualize this problem.
Click on the link to the right to view the full version of the eTool: Calc 4-12 eTool