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? 10 in. 2 in. 6 in. 352 square inches 372 square inches 392 square inches 432 square inches 6 in. 4 in. 10 in.

Explanation:

Step1: Calculate bottom layer surface area

First, find the total surface area of the bottom rectangular prism, then subtract the base (which is not frosted) and the area where the top layer sits.
Total surface area of bottom prism: $2(lw + lh + wh) = 2(10\times4 + 10\times6 + 4\times6) = 2(40+60+24)=2\times124=248$ square inches.
Subtract the base area ($10\times4=40$) and the overlapping area ($10\times2=20$): $248 - 40 - 20 = 188$ square inches.

Step2: Calculate top layer surface area

Find the total surface area of the top rectangular prism, then subtract the area where it sits on the bottom layer.
Total surface area of top prism: $2(lw + lh + wh) = 2(10\times2 + 10\times6 + 2\times6)=2(20+60+12)=2\times92=184$ square inches.
Subtract the overlapping area ($10\times2=20$): $184 - 20 = 164$ square inches.

Step3: Sum the frosted areas

Add the frosted areas of both layers: $188 + 164 = 372$ square inches.

Answer:

372 square inches