let

h = the height of the cylinder

r = 20 ft the radius of the cylinder

the volume of the cylinder is:

V = r^2 pi h

V = 20^2 pi h ft^2

A tank is to be constructed to hold 500,000 gallons when filled.

First we will convert 500,000 gallons to ft^3:

1 gal = 0.133681 ft^3

500,000 gal = 500,000*0.133681 ft^3 = 66840.5 ft^3

This is also the volume of the cylinder thus we have:

20^2 pi h = 66840.5

h = 66840.5/(20^2 pi)

pi = 3.14

h = 66840.5/(400*3.14)

h = 53.217 ft

Costs to construct the cylindrical portion will be $300/ft in height thus the total cost will be:

h*300 = 53.217*300 = $15,965.1.