Respuesta :
The dimensions of the tank with minimum weight are 24*24*12 ft
What is rectangular tank?
There is a benefit to employing vertical cylindrical stores that are put behind the double glass as in the Trombe wall system because a rectangular tank that extends from floor to ceiling is relatively expensive to construct and must be constructed to withstand quite high hydraulic pressures.
The tank with minimum weight is the one with minimum surface area.
Let x= base width and base height
h= height of the tank
The volume of tank is :
v=hx²
substitute v=6912 ft³
6912=hx²
h= 6912/x²............(1)
Formula for the tank surface area is:
A=x²+4xh
On substituting h value and simplifying,
A=x²+(27.648/x)
Differentiate with respect to x and equate to zero
2x-(27.648/x²)=0
On simplifying,
x³=27648/2 = [tex]\sqrt[^3]{13824}[/tex]
x= 24
substitute x=24 into the equation 1
h= 6912/(24)²= 12 ft
So, the dimensions of the tank with minimum weight are 24*24*12 ft
To learn more about the rectangular tank from the given link
https://brainly.com/question/28520375
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