PSAT Math Question: 2005 Alternate Exam

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1

<p>"What is the volume, in cubic inches, of the smallest rectangular box into which a 1-inch, 2-inch, and 3-inch cube can be placed (Assume the cubes are solid)?</p>

<p>A. 125
B. 75
C. 54
D. 45
E. 36</p>

<p>If you place the 1-inch cube and 2-inch cube adjacent to each other on top of the 3-inch cube, two of the box's dimensions are 3 and 5. But because of my poor spatial abilities, I can't figure out whether the remaining dimension is 3 inches or 5 inches. If anyone knows whether the correct answer is B (3 X 5 X 5) or D (3 X 5 X 3), please let me know. My guess is D.</p>

2

<p>If you look at the construction you designed from above, you'll see that both smaller cubes are sitting inside of the perimeter of the 3x3 side of the big cube.
You guess D (3x3x5) is correct.</p>