<p>Here is the question:</p>
<p>What is the volume, in cubic inches, of the smallest rectangular box into which a 1-inch cube, a 2-inch cube, and a 3-inch cube can be packed together?</p>
<p>A. 125
B. 75
C. 54
D. 45
E. 36</p>
<p>Correct Answer: D</p>
<p>Here's what I tried to do. I found the volume of the 3 small cubes came to a sum of 36 (Cube volume formula is e^3). Therefore, I assumed that the answer was 36. I've tried to find out what I am missing, but still am clueless on this problem. If someone could briefly it explain to me, I'd REALLY appreciate it.</p>
<p>All the best,
Robbie</p>
<p>Well, the box has to be rectangular. You can pack the three cubes into a container of 36 square inches, but it would have an odd shape. Imagine you have a 3-inch cube and want to add a 2-inch cube to it; if you place them side by side, then their combined base is 5 inches and their combined height (and width) is 3 inches. Then, you can add the 1-by-1 cube above the 2-by-2 cube. Consequently, the optimal rectangular prism that can envelop those 3 cubes is 5-by-3-by-3, or 45 cubic inches in volume.</p>
<p>You forgot to take into account the empty space in the rectangular box. You need to add the empty space in said box, therefore a completely different approach (supplied by Begoner) is needed.</p>
<p>This question is relatively easy. Do what Begoner said. I guess it would help if you try drawing it.</p>
<p>Great! Thx so much for the help guys. Btw, ya this is probably an easy question compared to the SAT. This was the “hard” math question on an old PSAT, which I am currently studying for.</p>