Answer:
The dimensions of the rectangular tank is 30.24 ft by 30.24 ft by 7.56 ft.
Step-by-step explanation:
Given that,
A rectangular tank is to be constructed with a square base and a volume of 6912 ft³.
Let length of the one side of the base be x and the height of the tank be y.
Then, the volume of the tank is= area of the base × height
=(x²)×y
=x²y ft²
Then,
x²y = 6912
The surface area of the tank is
= surface area of the sides + surface area of the base
=4(xy)+x² [ surface area of each wall= length × width =xy]
=4xy+x²
A= 4xy + x²
Plug in the above expression
Differentiating with respect to x
Again differentiating with respect to x
For maximum or minimum, A'=0
⇒x ≈ 30.24
Now
So, at x=30.24 ft the surface area minimum.
The length of one side of the base of the tank is = 30.24 ft
Then the height of the rectangular tank is
=7.56 ft
The dimensions of the rectangular tank is 30.24 ft by 30.24 ft by 7.56 ft.