Question

An open-top box is to be constructed from a 6 in by 2 in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let x denote the length of the side of each cut-out square. What is the volume?

Answer 1

Volume`=x^3-16x^2+12x`

Explanation:

Height of box: `=x`
Length of box: `=6-2x`
Width of box: `=2-2x`

Volume of box:
`x*(6-2x)(2-2x)`
`color(white)("XXX")=x*(12-16x+4x^2)`
`color(white)("XXX")=x^3-16x^2+12x`

Answer 2

Volume of open-top box would be `4x^3-16x^2+12x`

Explanation:

As `x` is the length of the side of each cut out square, the height of the open=top box will be `x`.

Its length will be `(6-2x)`

and width would be `(2-2x)`

Hence volume would be

`x(6-2x)(2-2x)`

= `x(12-12x-4x+4x^2)`

= `x(12-16x+4x^2)`

= `12x-16x^2+4x^3`

or `4x^3-16x^2+12x`