The surface area of a cylinder is given by the formula \(S= 2\pi r^{2}+2\pi rh\) where r is the radius of the circular base and h is the height of the cylinder.

Since the diameter of the tank is \(d=36\) ft, then the radius \(r=d\div2=36\div2=18 ft\).

Since we know the surface area is \(S=4750.1 ft^{2}\) and the radius is r=18, we can then substitute these values into the surface area formula to solve for h:

\(S= 2\pi r^{2}+2\pi\ rh\ \text{Surface are formula.}\)

\(4750.1= 2\pi(18)^{2}+2\pi(18)h\ \text{Substitute S}= 4750.1\ and\ r=18.\) \(4750.1= 2\pi(324)+36\pi h\ \text{Simplify.}\) \(4750.1= 648\pi+36\pi h\ \text{Simplify.}\) \(4750.1-648\pi= 36\pi \ Substract\ 648\pi\ on\ both\ sides.\) \((4750.1-648\pi)/(36\pi)=h\ Divide\ both\ sides\ by\ 36\pi.\) \(24\approx h\ \text{Evaluate using a calculator.}\) The height of the cylinder is then 24 ft.