Answer:
192 unit cubes.
Step-by-step explanation:
Let n represent number of cubes with each side 1/4 unit.
We have been given that a rectangular prism with a volume of 3 cubic units is filled with cubes with side lengths of 1/4 unit. We are asked to find the number of cubes that will fill that prism.
First of all, we will find volume of each cube.
[tex]\text{Volume of cube}=\text{Side length}^3[/tex]
[tex]\text{Volume of cube}=(\frac{1}{4}\text{ unit})^3[/tex]
[tex]\text{Volume of cube}=\frac{1^3}{4^3}\text{ unit}^3[/tex]
[tex]\text{Volume of cube}=\frac{1}{64}\text{ unit}^3[/tex]
The volume of rectangular prism will be equal to volume of n cubes.
[tex]\text{Volume of n cubes}=\text{Volume of rectangular prism}[/tex]
[tex]n\times \frac{1}{64}\text{ Unit}^3=3\text{ Unit}^3[/tex]
[tex]n\times \frac{1}{64}=3[/tex]
[tex]n\times \frac{1}{64}\times 64=3\times 64[/tex]
[tex]n=192[/tex]
Therefore, it will take 192 unit cubes to fill the prism.
