Answer:
448 half inch cubes can fit in the box.
Step-by-step explanation:
A box is represented by a parallelepiped, whose volume ([tex]V[/tex]), measured in cubic inches, is represented by the following formula:
[tex]V = w\cdot h\cdot l[/tex] (1)
Where:
[tex]w[/tex] - Width, measured in inches.
[tex]h[/tex] - Height, measured in inches.
[tex]l[/tex] - Length, measured in inches.
If we know that [tex]w = 4\,in[/tex], [tex]l = 4\,in[/tex] and [tex]V = 56\,in^{3}[/tex], then the height of the box is:
[tex]h = \frac{V}{w\cdot l}[/tex]
[tex]h = \frac{56\,in^{3}}{(4\,in)\cdot (4\,in)}[/tex]
[tex]h = 3.5\,in[/tex]
Given that box must be fitted by half inch cubes, the number of cubes per stage is:
[tex]x_{S} = \frac{(4\,in)\cdot (4\,in)}{(0.5\,in)\cdot (0.5\,in)}[/tex]
[tex]x_{S} = 64[/tex]
The number of stages within the parallelepiped is:
[tex]x_{N} = \frac{3.5\,in}{0.5\,in}[/tex]
[tex]x_{N} = 7[/tex]
The total quantity of half inch cubes that can fit in the box is:
[tex]n = x_{S}\cdot x_{N}[/tex]
[tex]n = (64)\cdot (7)[/tex]
[tex]n = 448[/tex]
448 half inch cubes can fit in the box.
