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Khi thinks that when the flags at right are rotated, the .

Decide if Khi 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:

Try computing the volume of each:

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:

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

Horizontal segment, with shaded right triangle labeled, A, above segment, with its short leg, labeled 3, on the right third of the segment, & vertical leg labeled, 4.

Horizontal segment, with horizontal rectangle labeled, C, above segment, with its bottom edge, labeled 3, on the right third of the segment, & right edge labeled 2, with shaded right triangle labeled, B, sharing its horizontal leg with top edge of rectangle, vertical leg  aligned with right edge of rectangle, labeled 4.