Question

What is the volume of a box that can fit exactly 128 1/8 inch cubes with 1/2 inch sides?

Answer 1

$\bf \textit{the volume of one small cube is }V=\left( \frac{1}{2} \right)\left( \frac{1}{2} \right)\left( \frac{1}{2} \right)\implies V=\cfrac{1}{8} \\\\\\ \textit{now, the box fits in }128\frac{1}{8}\textit{ of those cubes, thus its volume is} \\\\\\ 128\frac{1}{8}\cdot \cfrac{1}{8}\implies \cfrac{128\cdot 8+1}{8}\cdot \cfrac{1}{8}\implies \cfrac{1025}{8}\cdot \cfrac{1}{8}\implies \cfrac{1025}{64}\implies 16\frac{1}{64}~in^3$