Problem:
A cubical cake with edge length inches is iced on the sides and the top. It is cut vertically into three pieces as shown in this top view, where is the midpoint of a top edge. The piece whose top is triangle contains cubic inches of cake and square inches of icing. What is ?
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Answer Choices:
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Solution:
The area of triangle is , and its hypotenuse has length . Triangle is similar to triangle and has a hypotenuse of , so its area is . The volume of the required piece is cubic inches. The icing on this piece has an area of square inches. Therefore .
The problems on this page are the property of the MAA's American Mathematics Competitions