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Ok, you need to find the area of the circular segment removed. All we have is the radius (13) and the segment height (7). Here's a calculator that will do it for you and take out a lot of the pain, giving you all the other variables. http://www.1728.com/circsect.htm
Segment area is given as 115.2 si, which gives a volume of 7130 ci, which is about 31 gallons, which leaves you with 111 gallons. Came up with the same thing you did, which must mean we both did it right.