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 432 square inches

Explanation:

Step1: Calculate bottom layer surface area

First, find the total surface area of the bottom rectangular prism, then subtract the base area (since it's 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 base area ($10\times4=40$) and the area covered by top layer ($10\times2=20$):
$248 - 40 - 20 = 188$ square inches.

Step2: Calculate top layer surface area

Find the total surface area of the top rectangular prism, then subtract the area that 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 bottom area of top layer ($10\times2=20$):
$184 - 20 = 164$ square inches.

Step3: Sum the frosted areas

Add the frosted area of the bottom layer and the top layer.
$188 + 164 = 352$ square inches.

Answer:

352 square inches