1997 AMC 8 Problem 17
Below is the professionally curated solution for Problem 17 of the 1997 AMC 8, 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.
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Difficulty rating: 1270
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?
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
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