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}* w* h`
`V=1*1(1)/(6)*2(1)/(6)`
`=1*(7)/(6)*(13)/(6)`
`=(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 =

`=(91)/(36)\text{ divide by }(1)/(216)`
`=(91)/(36)*(216)/(1)`
`=(19656)/(36)`
`=546`