Question

How many cubes with side lengths of 1/2 cm does it take to fill up the prism

Answer 1

24 cubes can filled up the prism

Solution:

The image of the question is attached below.

Given data:

Length of the prism = 2 cm

Breadth of the prism = 1 cm

Height of the prism =
`$(3)/(2)` cm

Volume of the prism = length × breadth × height

`$=2* 1* (3)/(2)`

`=3` cubic cm

Volume of the prism = 3 cubic cm

Side length of the cube =
`$(1)/(2)` cm

Volume of the cube = side × side × side

`$=\left((1)/(2)\right)^(3)`

`$=(1)/(8)` cubic cm

Volume of the cube =
`(1)/(8)` cm

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

`$=(3)/((1)/(8) )`

`=3*8`

`=24`

Number of cubes = 24

Hence 24 cubes can filled up the prism.