CPM Homework Help : CALC Problem 4-12

Khi thinks that when the flags below are rotated, the (volume of $A$ ) $+$ (volume of $C$ ) $=$ (volume of ( $B + C$ )).

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

Hint 1:

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

Answer 1:

Volume $A$ is cone with radius $4$ . Volume $C$ is a cylinder with radius $2$ . Each is a separate 3D solid whose volumes are added together after they are computed: $V =$ [cone with $r = 4$ ] + [cylinder with $r = 2$ ]

Hint 2:

Try computing the volume of each:
Volume $A +$ Volume $C =$ cone $+$ cylinder
Volume $(B + C) =$ BigCone − SmallCone
Evaluate and compare.

Answer 2:

Volume ( $B + C$ ) 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:
$V =$ [large cone with $r = 6$ ] $−$ [small cone with $r = 2$ ]

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