1997 AMC 8 Problem 17
Attempt Problem 17 of the 1997 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 1997 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
17.
A cube has eight vertices (corners) and twelve edges. A segment, such as which joins two vertices not joined by an edge is called a diagonal. Segment is also a diagonal. How many diagonals does a cube have?
Answer: E
Small hint:
Each face has two diagonals, and opposite vertices give space diagonals
Big hint:
Count face diagonals and space diagonals separately
Solution:
Each face has two diagonals connecting each of the two pairs of opposite vertices.
Also, for each vertex, there is one corresponding vertex that lies opposite it on the cube.
There are then interior space diagonals in the cube.
The total number of diagonals is then
Thus, E is the correct answer.
Problem 17 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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