Answer: There are 160 plastic cubes that can fit into the box.
Step-by-step explanation:
Since we have given that
Length of box = 4 ft
Width of box = 212 ft
Height of box = 2 ft
As we know that the formula for "Volume of cuboid":
[tex]Volume=Length\times Width\times Height\\\\Volume=4\times 2\frac{1}{2}\times 2\\\\Volume=4\times \frac{5}{2}\times 2\\\\Volume=20\ ft^3[/tex]
And we have
Edge length of each plastic = [tex]\frac{1}{2}\ ft[/tex]
As we know that the formula for "Volume of cube":
[tex]Volume=Side^3\\\\Volume=\frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\\\\Volume=\frac{1}{8}\ ft^3[/tex]
So, Number of plastic cubes can fit into the box is given by
[tex]\frac{\text{ Volume of box}}{\text{ Volume of plastic cube}}\\\\=\frac{20}{\frac{1}{8}}\\\\=20\times 8\\\\=160[/tex]
Hence, there are 160 plastic cubes that can fit into the box.
