I know that there are 231 cubic inches in an American gallon so I will change all your measurements to inches. There are 12 inches in a foot so the depth of water in the well is
12 8 = 96 inches.
The volume of a circular cylinder is r2 h where r is the radius and h is the height. Thus the volume of water in your well is
r2 h = 152 96 = 67858 cubic inches.
There are 231 cubic inches in a gallon so this is
67858/231 = 294 gallons.