Question

A rectangular tank that is with a square base and open top is to be constructed of sheet steel of a given thickness. find the dimensions of the tank with minimum weight.

Answer 1

The dimensions of the tank with minimum weight are; 26 ft by 26 ft by 13 ft.

How to minimize functions?

For minimum weight, it means that the surface area must be minimum.

Let the height be h and the lengths be x

Thus, the volume is;

x²h = 8788

Thus;

h = 8788/x²

Surface Area is;

A = x² + 4xh

A = x² + 35142/x

dA/dx = 2x - 35152/x²

When dA/dx = 0, we have;

2x - 35152/x² = 0

2x  =35152/x²

Thus;

2x³ = 35152

x³ = 17576

x = 26 ft

Thus;

h = 8788/x²

h = 8788/26²

h = 13 ft

Thus, the dimensions are 26 ft by 26 ft by 13 ft.

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