Problema Solution
A one-cubic foot is cut into 4 pieces by 3 cuts parallel to the top face of the cube. The first cut is a half foot from the top face. The second cut is one third foot below the first cut, and the third cut is one seventeenth foot below the second cut. From the top to the bottom the pieces are labeled A, B, C and D. The pieces are then glued together end to end in the order of C, B, A, D to make a long solid as shown below. What is the total surface area of the solid in square feet?
Answers: A)6 B)7 C)419/51 D)158/17 E)11
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Also the sides of a 1 cubic foot block would each have a surface area of (1/4) square inches and you couldn't make that first cut - there wouldn't be enough wood. I'm going to assume that you meant to say a block each of whose edges is one foot and thus each if it's face would be one foot by one foot. Otherwise the problem makes no sense at all.
The sides that are partial only, the last one D doesn't look partial still add up to a total area of one square foot.
C, the leftmost block has a side fact of one square foot. It also a top, a side pointing forward and a side pointing backward, and so do all of the other. Each of those sets of three faces adds up to 3 square feet and since there are four blocks, it totals 12 square feet. The leftmost side of the block C is another square foot as mentioned above and that gets us up to 13 square feet. Furthermore, the total exposed wood on the right is one square foot - it's sliced up but it is one square foot and that gets us up to 14 square feet.
The answer is 14 square feet.