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( (1)/(2) \right)\left( (1)/(2) \right)\left( (1)/(2) \right)\implies V=\cfrac{1}{8} \\\\\\ \textit{now, the box fits in }128(1)/(8)\textit{ of those cubes, thus its volume is} \\\\\\ 128(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(1)/(64)~in^3`