Math Is Fun Forum

taylor_2009

Member

Registered: 2010-01-25

Posts: 28

Find dimensions of a closed rectangular box?

Find the dimensions of a closed rectangular box with a square base and volume 125 in³ that can be constructed from the least amount of material.

What are the dimensions of the box?
The length of one side of the base is _____ in.
The height of the box is _____ in.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Find dimensions of a closed rectangular box?

Hi taylor_2009;

The Volume of the box l * w * h and since l = w we can say V = w^2 *h

The amount of material is equal to the Total area of all the sides of the closed box.

A = 2 w^2 + 4 * h * w

V = w^2 *h  = 125

Solve for h:

h = 125 / w^2 and plug in to the area equation.

Minimize the area:

So w = 5, l = 5 and h = 125 / w^2 = 5

We have a 5x5x5 cube.

Graph the equation 

  to check that at w = 5 we have a minimum.

http://www.mathsisfun.com/graph/functio … 5992080962

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