1990 AJHSME Problems/Problem 18

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?

$[asy] draw((0,0)--(3,0)--(3,3)--(0,3)--cycle); draw((3,0)--(5,2)--(5,5)--(2,5)--(0,3)); draw((3,3)--(5,5)); draw((2,0)--(3,1.8)--(4,1)--cycle,linewidth(1)); draw((2,3)--(4,4)--(3,2)--cycle,linewidth(1)); [/asy]$

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

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 $\rightarrow \boxed{\text{C}}$ .

1990 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 17	Followed by Problem 19
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1990 AJHSME Problems/Problem 18

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