Let's draw the figure to better understand the scenario:
Since the cardboard is a "square", all sides must be equal.
The drawing above shows what the sections would look like.
Let's now draw what the box would look like after being cut 4 in. x 4 in. on each corner.
The cardboard formed appears to have the following dimensions:
Length = x - 8
Width = x - 8
Height = 4
In getting the volume of the box, we will be using the following equation:
[tex]\text{ Volume = Length x Width x Height}[/tex]
We get,
[tex]\text{ Volume = (x -8)(x - 8)(4) = (4)\lbrack(x - 8)}^2\rbrack[/tex][tex]\text{ = (4)\lbrack(x)(x) + (x)(-8) + (-8)(x) + (-8)(-8)\rbrack}[/tex][tex]\text{ = 4(x}^2\text{ - 8x - 8x + 64) = 4(x}^2\text{ - 16x + 64)}[/tex][tex]\text{ Volume = 4x}^2\text{ - 64x + 256}[/tex]
Therefore, the equation to determine the volume of the box is:
Volume = V = 4x² - 64x + 256
