### Home > CALC > Chapter 4 > Lesson 4.1.1 > 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. Homework Help ✎

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