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...

       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 the box is 500 cm3, find the dimensions of the original metal sheet.

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lemjay | High School Teacher | (Level 3) Senior Educator

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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.

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