Answer: 360
Step-by-step explanation:
Given
the side length of the cube [tex]a=\frac{1}{4}\ inch[/tex]
The dimension of the box is [tex]1\times3 \frac{3}{4}\times 1 \frac{1}{2}=1\times\frac{15}{4}\times\frac{3}{2}\ inch^3[/tex]
the volume of each cube [tex]=a^3=(\frac{1}{4})^3[/tex]
No. of cubes that can be fit into the box [tex]=\dfrac{\text{vol. of box}}{\text{vol. of each cube}}[/tex]
[tex]\Rightarrow \dfrac{1\times \frac{15}{4}\times\frac{3}{2}}{\frac{1}{4}\times\frac{1}{4}\times\frac{1}{4}}=360[/tex]
Therefore 360 cubes can be fit into the box
