  ### Home > CALC > Chapter 4 > Lesson 4.1.1 > Problem4-12

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.

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?

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 $r = 2$]

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

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