Question

The dimensions of a right rectangular prism are shown below. 1 in. 1a in. 2 in. in. How many cubes with side lengths of inch are needed to fill the prism without gaps or overlaps?

Answer 1

First we neeed to find the volume of the rectangular prism

$V=\text{ l}\times w\times h$$V=1\times1\frac{1}{6}\times2\frac{1}{6}$$=1\times\frac{7}{6}\times\frac{13}{6}$$=\frac{91}{36}in^3$

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 =

$=\frac{91}{36}\text{ divide by }\frac{1}{216}$$=\frac{91}{36}\times\frac{216}{1}$$=\frac{19656}{36}$$=546$