A rectangular tank with a square base, an open top, and a volume of 6912 ft^2 is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective function.A= _____ (type an expression)The tank with the minimum surface area has a height of ___ ft and a square base with a sidelength of ___ ft.

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Asked Oct 29, 2019
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A rectangular tank with a square base, an open top, and a volume of 6912 ft^2 is to be constructed of sheet steel. Find the dimensions of the tank that has the minimum surface area.

Let s be the length of one of the sides of the square base and let A be the surface area of the tank. Write the objective function.

A= _____ (type an expression)

The tank with the minimum surface area has a height of ___ ft and a square base with a sidelength of ___ ft.

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Expert Answer

Step 1

Given tank is open at top.

So, the surface area is,

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A =s2+4sh Then, the volume is, V 6912 s2h 6912 6912 h =

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Step 2

Find the minimum surface...

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6912 6912 A(s) s2+4s h= 27648 27648 A(s) 2s- 2s3-27648 Equate A' (s) 0 2s3-27648 2s3-27648 0 27648 13824 s 24

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