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Calculus/Dimension Applications of Derivatives

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Expert: - 1/11/2009


Question
Find the dimensions of the largest open-top storage bin with a square base and vertical sides that can be made from 108ft^2 of sheet steel. (neglect the thickness of the steel and assume that there is no waste.)

Answer
We've got to assume something, so lets assume that the base has width B and the height is H.  The total surface area is the the base plus the four sides.  The base has area B².  The sides have area BH, and there are four of them.  B² + 4BH is the total area, and this is suppose to be 108 ft².

The volume is [A] V = B²H.  H can be solved for from the equation
for surface area and put into [A] so that B is the only variable.

Take the derivative of volume, getting dV/DB , and set it equal to 0.

This will give the length of the base B with the largest volume V.

From there we can get both H and V.

Calculus

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