Answer:
Given number of gallon tank = 3600
We have to find the size of tank that should be ordered.
Step-by-step explanation:
Since we know that, 1 gallon = 0.133681 ft^3
3600 gallons = 481.25 ft^3
Volume = πr^2 h
πr^2 h = 481.25
h = 481.25 / πr^2
Surface are = 2πrh + 2πr^2
Now insert values, A = 2πr (481.25 / πr^2) + 2πr^2
A = 2πr (481.25 / πr^2) + 2πr^2
A = 962.5 / r + 2πr^2
For minimum surface area.
dA / dr = 0
962.5 / r^2 + 4πr = 0
962.5 / r^2 = 4πr
962.5 = 4πr^3
r^3 = 76.56
r = 4.25
The radius of cylinder = 4.25 ft
Height = 481.25 / πr^2
Height = 481.25 / π(4.25)^2
Height = 8.48 ft.
