1991 AMC 8 Problem 15
Attempt Problem 15 of the 1991 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 1991 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
15.
All six sides of a rectangular solid were rectangles. A one-foot cube was cut out of the rectangular solid as shown. The total number of square feet in the surface of the new solid is how many more or less than that of the original solid?
less
less
the same
more
more
Answer: C
Small hint:
Cutting the cube removes some faces that were on the surface but uncovers new ones; compare the two amounts
Big hint:
The cube’s top, front, and back faces were on the surface ( square feet removed); the notch’s floor and its two side walls become new surface ( square feet added)
Solution:
The removed cube had three faces on the surface of the solid (top, front, and back), so square feet of surface are removed.
Cutting it out exposes three new faces (the floor of the notch and its two side walls), adding square feet. The surface area is unchanged.
Thus, the correct answer is C .
Problem 15 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1992 AMC 8
- 1993 AMC 8
- 1994 AMC 8
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