Cool sum in hot summer

Geometry Level pending

A $(8 \times 6 \times 4) \text{cm}^3$ metallic cuboid is melted. Find the minimum volume of molten metal which should be added to mold it into a cube whose edge is $X$ , where $X$ is an integer.

23 22 24 20 21

1 solution

Marta Reece
May 9, 2017

$8\times6\times4=192$

We are looking for an integer which if raised to a third power will give us little more than $192$ . To find such integer, we can take a third root of $192$ , which is approximately $5.77$ . So the next higher integer is $6$ .

$6^3-192=\boxed{24}$

Cool sum in hot summer

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