1 Answer

Nikitz · Answer 1 · 2022-02-09T06:29:04+0000

Answer:

448 half inch cubes can fit in the box.

Explanation:

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

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

Where:

- Width, measured in inches.

- Height, measured in inches.

- 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:

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

$h = (56\,in^(3))/((4\,in)\cdot (4\,in))$

$h = 3.5\,in$

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

$x_(S) = ((4\,in)\cdot (4\,in))/((0.5\,in)\cdot (0.5\,in))$

x_(S) = 64

The number of stages within the parallelepiped is:

$x_(N) = (3.5\,in)/(0.5\,in)$

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.

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