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.

Question

Mathematics

Leonard Santiago

4 March, 05:09

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.

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Answers (1)

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Lamont Walls · Answer 1

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

Step-by-step 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)