CK5
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Volume calculation assistance! Picture added.

Now there's some trig involved in this one, let me see what I can dig up. You're on the right track with 142 gallons to start...
 
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. ;)
 
Yep, I think we're good to go. 111 it is. I finally got Autocad to verify it as well.
 
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