A square sheet of metal is made into an open box by cutting 5 cm by 5 cm squares out of each corner (see diagram) and bending up the sides (along the dashed lines). If the volume of...

Let x be the sides of the square metal sheet.

Since `5xx5` cm is cut on each corner of the metal sheets to form an open box, then the dimensions of the box is:

length = x-10

width  = x-10        and

height = 5

Since the volume of the box is given, apply the formula of volume to solve for x.

`V=l*w*h`

`500=5(x-10)(x-10)`

To simplify, divide both sides by 5.

`500/5=(5(x-10)(x-10))/5`

`100=(x-10)(x-10)`

FOIL right side.

`100=x^2-10x-10+100`

`100=x^2-20x+100`

Set one side equal to zero.

`100-100=x^2-20x+100-100`

`0=x^2-20x`

Then, factor right side.

`0=x(x-20)`

Next, set each factor equal to zero and solve for x.

`x=0`           and          `x-20=0`

                                         `x=20`

Since x represents the length of the sides of the square metal sheet, consider only the value of x that is greater than zero.

Hence, the dimension of the square metal sheet is `20xx20` cm.