# Ice in a refrigerator (packing cubes in a box) .. Check

A refrigerator is 8 inches long , 4 inches wide and 5 inches high.How many ice cubes will it hold if each cube is 2 inches on the edge.

According to me its 20 because volume of Fridge = 160 and volume of cube=8 so 160/8 = 20 However the books says the answer is 24. Am i missing something or is this a misprint ?

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A complicating factor is that you cannot fill the 5 inches of height perfectly, since you presumably don't want to slice up the cubes. – akkkk Jun 28 '12 at 12:16
It's important to develop the habit of "sanity-checking" problems like this for physical constraints you might have missed. As we see here, blindly applying the math can lead to wrong results. – rschwieb Jun 28 '12 at 12:18
So the books answer is then completely off since its assuming more cubes that i have calculated ?? – Rajeshwar Jun 28 '12 at 12:19
Smallest refrigerator I ever heard of. And if it's about ice cubes, a freezer would be a better idea. – Gerry Myerson Jun 28 '12 at 13:09
@Rajeshwar: Your reasoning is only partly right. By volume considerations, the answer is clearly $\le 20$. In fact it is less than $20$, because of the $5$ inch part. We can certainly fit in $16$. Perhaps one can fit in one more by using a strange packing. Certainly one can if we replace $5$ by $5.9$. – André Nicolas Jun 28 '12 at 17:56

You can get only $\frac{8}{2}$ times $\frac{4}{2}$ times the floor value of $\frac{5}{2}$, which is $2$ inside. This means a total of $16$ ice cubes.