Question
Asked Nov 21, 2019
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a rectangular tank that is 864 ft cubed 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

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Expert Answer

Step 1

Let the measure of side of square base of tank  is x ft and height of tank is y ft and volume of tank is 864 cubic ft. Then we have

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V =xy x2y 864 864 y =

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Step 2

The problem is to minimize the surface area of tank. Surface area of tank is given by

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s x24xy 864 4х. S x2 3456 х

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Step 3

Now, we find dS/dx and so...

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ds 2x dx 3456 = 0 ds - 2x dc 3456 = 0 x31728 x 12

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Math

Calculus

Derivative

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