Question

A cake is created by assembling two layers as shown in the diagram below. The exposed surfaces of the cake require frosting.



Assuming the 4 inch by 10 inch base on which the cake sits will not be frosted, what is the area that will require frosting?

352 square inches
372 square inches
392 square inches

Answer 1

I can’t see the diagram you mention, so I don’t have the exact dimensions and placement of the two layers. Could you either upload the picture or describe the two rectangular blocks (length × width × height for each) and how the top layer is positioned on the bottom layer (centered, flush with one side, offset by some amount, etc.)?

If you’d rather solve it yourself, here’s the method to use once you have those details:

1. Compute the total surface area of each rectangular block (2(lw + lh + wh)).
2. Add the surface areas of the two blocks.
3. Subtract twice the area of any faces that are glued together between the blocks (because those faces are not exposed).
4. Subtract the bottom area (4 in × 10 in = 40 in²) because the base on which the cake sits is not frosted.
5. The result is the exposed area that needs frosting.

If you give the block dimensions and the overlap region (or upload the diagram), I’ll compute the exact frosting area and pick the correct choice.