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1990 AJHSME Problems/Problem 18

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Problem

Each corner of a rectangular prism is cut off. Two (of the eight) cuts are shown. How many edges does the new figure have?

draw((0,0)--(3,0)--(3,3)--(0,3)--cycle);draw((3,0)--(5,2)--(5,5)--(2,5)--(0,3));draw((3,3)--(5,5));draw((2,0)--(3,1.8)--(4,1)...

\text{(A)}\ 24 \qquad \text{(B)}\ 30 \qquad \text{(C)}\ 36 \qquad \text{(D)}\ 42 \qquad \text{(E)}\ 48

Assume that the planes cutting the prism do not intersect anywhere in or on the prism.

Solution

In addition to the original 12 edges, each original vertex contributes 3 new edges.

There are 8 original vertices, so there are 12+3\times 8=36 edges in the new figure \rightarrow \boxed{\text{C}}.

See Also

1990 AJHSME (Problems • Resources)
Preceded by
Problem 17 		Followed by
Problem 19
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25
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