Question

How many cubes with side lengths of 1/3 cm does it take to fill the prism?

Length 1 cm, Width 2 2/3, Height 2/3

Answer 1

The number of cubes that fill the prism is 24

Explanation:

Given as :

The length of cube (l) =
`(1)/(3)` cm

The length of prism (L) = 1 cm

The width of prism (w) = 2
`(2)/(3)` =
`(8)/(3)` cm

The height of prism (h) =
`(2)/(3)` cm

Let the number of cubes that fill the prism = x

Now, Volume of cube with length (l) = l³ cm³

Or, Volume of cube with length (l) =
`((1)/(3))^(3)` cm³

Or, Volume of cube with length (l) =
`((1)/(27))` cm³

Again , Volume of prism =
`(1)/(2)* Length * width * height`

Or, Volume of prism =
`(1)/(2)* 1 * (8)/(3) * (2)/(3)`

Or, Volume of prism =
`((8)/(9))` cm³

So , The number of cubes to fill prism

The number of cubes × Volume of cube = Volume of prism

Or, x ×
`((1)/(27))` cm³ =
`((8)/(9))` cm³

or x =
`(8* 27)/(9)` = 24

Hence The number of cubes which fill the prism is 24 Answer