Question

An open box is to be made from a flat piece of material 19 inches long and 3 inches wide by cutting equal squares of length xxfrom the corners and folding up the sides. Write the volume VVof the box as a function of xx. Leave it as a product of factors, do not multiply out the factors.

Answer 1

V=x(19-2x)(3-2x)

Explanation:

The flat piece of material is 19Inches Long and 3 Inches Wide.

If we cut a square if length x from each corner:

Length if the Box=19-x-x=19-2x

Width if the Box=3-x-x=3-2x

The flap that will be folded up will be the height.

Therefore, Height of the Box= x inches.

Volume of a cuboid=lwh

Therefore the volume of the box will be:

V=x(19-2x)(3-2x)