# Box Mystery

Geometry Level 4

There are 6 identical square sheets of paper, each with an area of $$a^2$$ for some positive integer $$a$$.

Instead of putting them together as a simple cube, these sheets are cut and taped to construct a cuboid of dimensions $$a\times b\times c$$ for some distinct positive integers $$a, b, c$$.

If the volume of the box equals $$9a^2$$, compute $$a+b+c$$.

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