1993 AMC 8 Problem 17

Attempt Problem 17 of the 1993 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1993 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

17.

Square corners, 55 units on a side, are removed from a 2020 unit by 3030 unit rectangular sheet of cardboard. The sides are then folded to form an open box. The surface area, in square units, of the interior of the box is
300300
500500
550550
600600
10001000
Answer: B
Concepts:surface areanet (3D geometry)
Small hint:
Folding does not change area; the interior surface equals the sheet minus the four corner squares
Big hint:
The sheet is 20×30;20 \times 30; subtract four 5×55 \times 5 corner squares
Solution:
The interior surface is exactly one face of the cardboard after the corners are removed. The sheet has area 20×30=600,20 \times 30 = 600, and each removed corner has area 5×5=25.5 \times 5 = 25.
So the interior surface area is 600−4×25=500.600 - 4 \times 25 = 500.
Thus, the correct answer is B .
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