Question

How many cubes with side lengths of 1/2 cm does it take to fill the prism?

Answer 1

Check the picture below.

so, let's get the volume of the prism.

then let's get the volume of the smaller cube.

then let's see how many times the volume of the cube goes into the prism's volume, so in short a division.

`\stackrel{\textit{prism's volume}}{\left( (5)/(2) \right)(2)(1)\implies 5~cm^3}~\hfill \stackrel{\textit{cube's volume}}{\left( (1)/(2) \right)\left( (1)/(2) \right)\left( (1)/(2) \right)\implies (1)/(8)~cm^3} \\\\[-0.35em] ~\dotfill\\\\ 5/ \cfrac{1}{8}\implies \cfrac{5}{1}/ \cfrac{1}{8}\implies \cfrac{5}{1}\cdot \cfrac{8}{1}\implies 40~~cubes`