Find the volume of a box as a function of the width of base of the box?

If 12,000 cm^2 of material is available to make a box with a square base and an open top, find the volume of the box as a function of the width if the base of the box

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- Sep 28th 2008, 07:09 PMrealintegerzVolume of a box?
Find the volume of a box as a function of the width of base of the box?

If 12,000 cm^2 of material is available to make a box with a square base and an open top, find the volume of the box as a function of the width if the base of the box - Sep 28th 2008, 08:04 PMJhevon
did you draw a diagram? (see the attached).

let the width of the base be and the height of the box be

thus the volume (length times width times height) is given by

Now we know the surface area is 12000, this is the sum of the areas of all the faces, so

that is

now can you answer the problem? - Sep 28th 2008, 08:13 PMSoroban
Hello, realintegerz!

Quote:

If 12,000 cm² of material is available to make a box

with a square base and an open top, find the volume of the box

as a function of the width of the base of the box.

Code:`*-------*`

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/ | / |

*-------* |

| | |

| | |

h| | *

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| |/ x

*-------*

x

Let = side of the square base.

Let = height of the box.

The panels comprising the box is made up of:

. . a base with area

. . and four sides with area each.

The total surface area is: .

We are told that the total surface area will be 12,000 cm².

So we have: . .[1]

The volume of the box is: .

Substitute [1]: .