Answer:
464 in²
Explanation:
Given the 10-inch cube bottom layer of a cake is topped by a 6-inch cube, you want to know the frosted area of the bottom layer.
Lateral area
The lateral area of the bottom cube is 4 faces, each of which is a 10-inch square. That lateral area is ...
4 × s² = 4 × (10 in)² = 400 in²
Top area
The top area of the bottom layer is the difference in area between a 10-inch square and a 6-inch square. That difference is ...
(10 in)² -(6 in)² = (100 -36) in² = 64 in²
Total frosting
The total frosted area is the sum of the lateral area and the top frosted area:
frosted area = 400 in² +64 in² = 464 in²
The area that will be frosted on the bottom layer is 464 square inches.
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