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