Given:
Cuboid:
[tex]\begin{gathered} Length,l=4\text{ inches} \\ Breadth,b=\frac{3}{4}\text{ inch} \\ Height,h=1\frac{2}{4}inches \end{gathered}[/tex]
Cube:
[tex]\text{Side, a}=\frac{1}{4}inch[/tex]
To find: The number of cubes required to pack the prism completely.
Explanation:
The formula is,
[tex]\begin{gathered} n=\frac{\text{Volume of cuboid}}{\text{Volume of cube}} \\ n=\frac{l\times b\times h}{a^3} \end{gathered}[/tex]
Substituting the given values in the above formula, we get,
[tex]\begin{gathered} n=\frac{4\times\frac{3}{4}\times1\frac{2}{4}}{(\frac{1}{4})^3} \\ =\frac{4\times\frac{3}{4}\times\frac{6}{4}}{\frac{1}{64}} \\ =\frac{\frac{9}{2}}{\frac{1}{64}} \\ =\frac{9}{2}\times\frac{64}{1} \\ =9\times32 \\ n=288 \end{gathered}[/tex]
Thus, the number of cubs required to pack the prism is 288 cubes.
Final answer: 288 cubes
