Question

a box has a volume of 56 cubic inches, and the base of the box is 4 inches by 4 inches. how many half inch cubes can fit in the box?

Answer 1

Answer:

448 half inch cubes can fit in the box.

Step-by-step explanation:

A box is represented by a parallelepiped, whose volume ($V$), measured in cubic inches, is represented by the following formula:

$V = w\cdot h\cdot l$ (1)

Where:

$w$ - Width, measured in inches.

$h$ - Height, measured in inches.

$l$ - Length, measured in inches.

If we know that $w = 4\,in$, $l = 4\,in$ and $V = 56\,in^{3}$, then the height of the box is:

$h = \frac{V}{w\cdot l}$

$h = \frac{56\,in^{3}}{(4\,in)\cdot (4\,in)}$

$h = 3.5\,in$

Given that box must be fitted by half inch cubes, the number of cubes per stage is:

$x_{S} = \frac{(4\,in)\cdot (4\,in)}{(0.5\,in)\cdot (0.5\,in)}$

$x_{S} = 64$

The number of stages within the parallelepiped is:

$x_{N} = \frac{3.5\,in}{0.5\,in}$

$x_{N} = 7$

The total quantity of half inch cubes that can fit in the box is:

$n = x_{S}\cdot x_{N}$

$n = (64)\cdot (7)$

$n = 448$

448 half inch cubes can fit in the box.