Question

A rectangular prism with a volume of 444 cubic units is filled with cubes with side lengths of \dfrac13

3

1

​

start fraction, 1, divided by, 3, end fraction unit.

How many \dfrac13

3

1

​

start fraction, 1, divided by, 3, end fraction unit cubes does it take to fill the prism?

Answer 1

108

Explanation:

Answer 2

108 cubes

Explanation:

Lengths of one of the cube s=
`(1)/(3)`

Volume of a Cube
`=s^3`

Volume of one of the Cubes
`=((1)/(3))^3=(1)/(27)`

The volume of the rectangular prism is 4 cubic units.

Therefore, to find the number of cubes it takes to fill the prism, we divide the volume of the prism by the volume of the cube.

`\text{Volume of Prism/Volume of Cube}=4 / (1)/(27)\\=4 X 27 \\=108`

It takes 108 cubes to fill the rectangular prism.