Bunuel wrote:
A box measuring 11 inches by 10 inches by 7 inches is filled with solid wooden cubical blocks, each measuring 3 inches per side. How many wooden blocks can fit into the box?
A. 18
B. 27
C. 28
D. 29
E. 54
Official solution from Veritas Prep.
This problem is tricky because you must think about it logically BEFORE you do the math. Mathematically, you can quickly calculate \(11∗10∗7=770\). Each cube has a volume of \(3∗3∗3=27\). This problem invites you to do the math \(\frac{770}{27}=28.5\). And if you've done that, choices C and D are waiting for you to determine whether to round up or down.
HOWEVER, you should not do the math before logically setting up the problem. Since you have solid wooden blocks, you will not be able to fit blocks across all levels. For instance, if one side measures 7 inches, only two blocks can fit. There will be 1 inch of wasted space. You will get only three blocks on each of the two remaining sides. Consequently, you will be able to fit \(2∗3∗3=18\) blocks inside the box.
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