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Calculus/pre calc word problem

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Expert: - 1/21/2008


Question
An open rectangular box with a square base is to have a volume of 15ft^3. find a function that models the surface area, A(x), of the box, where x is the length of one side of the base. Find the box dimensions that minimize the amount of material used to make the box. Round your dimensions to the nearest hundredth.

Answer
The box has a height h, a depth d, and a width w.  The surface area is the area of the four sides plus the area of the bottom.  The volume is defined to be 15ft^3.

Hence there are three unknown in the original problem.

The variable w = d, since it has a square base.  
The variable h can be found in terms of w since hw^2=15.

The problem has been reduced expressing the surface area to a problem with only one variable, w.

To maximize this, find the derivative and set it equal to 0.

Calculus

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