Question

A rectangular prism with a volume of four cubic units is filled with cubes with side lengths of 1/3 unit.

how many 1/3 unit cubes does it take to fill the prism?

Answer 1

Given:

Volume of rectangular prism = 4 cubic units

Side length of cube =
`(1)/(3)` unit

To find:

How many cubes fill in the prism.

Solution:

Volume of cube = side × side × side

`$=(1)/(3) * (1)/(3) * (1)/(3)`

`$=(1)/(27)`

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

`$=(4)/((1)/(27) )`

Apply the fraction:
`(a)/((b)/(c))=(a \cdot c)/(b)`

`$=(4 \cdot 27)/(1)`

Number of cubes = 108

Therefore 108 cubes fill in the prism.