Question

How many cubes are needed to fill in the rectangular prism?

Answer 1

8320 cubes can fit into the prism.

Solution:

Convert mixed fraction into improper fraction.

Length of the prism = 20 in

Width of the prism = 2 in

Height of the prism =
`3(1)/(4)=(13)/(4)` in

Volume of the prism = length × width × height

`$=20*2*(13)/(4)`

= 130 in³

Volume of the prism = 130 in³

Length of the cube =
`(1)/(4)` in

Volume of the cube = length × length × length

`$=(1)/(4) *(1)/(4) *(1)/(4)`

`$=(1)/(64) \ \text{in}^3`

Volume of the cube = 0.015625 in³

`$\text{Number of cubes}=\frac{\text{Volume of the prism}}{\text{Volume of cube}}`

`$=(130)/(0.015625)`

= 8320

Number of cubes = 8320

Hence 8320 cubes can fit into the prism.