First we neeed to find the volume of the rectangular prism
[tex]V=\text{ l}\times w\times h[/tex][tex]V=1\times1\frac{1}{6}\times2\frac{1}{6}[/tex][tex]=1\times\frac{7}{6}\times\frac{13}{6}[/tex][tex]=\frac{91}{36}in^3[/tex]
Volume of cube with side lengths 1/6 = 1/6 x 1/6 x 1/6 = 1/216
The number of cubes needed to fill the prism without gaps or overlaps =
[tex]=\frac{91}{36}\text{ divide by }\frac{1}{216}[/tex][tex]=\frac{91}{36}\times\frac{216}{1}[/tex][tex]=\frac{19656}{36}[/tex][tex]=546[/tex]
