Boring a cylinder is usually for the sole purpose of making it cylindrical again. As an engine is run, the upper part of the cylinder slowly wears more than the bottom, leading to a condition known as taper - the cylinder is a little wider at the top than at the bottom. This leads to poor sealing at the top - which is, of course, where combustion occurs and where most of the work of the expanding gases is done. Poor ring seal leads to lower power and increased oil consumption. When an engine is rebuilt, the cylinders are measured for taper - how much larger the cylinder is at the top than the bottom - and if it's beyond factory specs, then the cylinders must be bored out to make them the same size from top to bottom. The amount of taper allowed is typically very small - only .010 inches (aka 1/100th of an inch) for a 360 - before the cylinder needs to be reconditioned.
In addition, the cylinder will also wear more to one side than the other, leading to the bore not being round - known as (not surprisingly) "out-of-round." Again, for a 360, it's only allowed to be .005 inches out-of-round - yes, 5/1000's of an inch.
When the cylinder is re-conditioned, the machinist will set the block up in a boring machine and overbore the cylinders a small amount. As HK said, common overbores are .030 and .060 over, although overbores of .020 and .040 are not uncommon. In other words, using a 360 as our base, the standard bore is 4.000 inches diameter (or 2.000 inch radius) and the standard stroke is 3.58 inches. Using the volume of the cylinder equation HK provided, that means each cylinder is 2 x 2 x 3.1415 x 3.58 = 44.99 cubic inches x 8 = 359.9 cubic inches. Going out the maximum allowable overbore of .040 inches, (See
http://www.angelfire.com/ca/mikesspot/360specs.html for specifications) means that each cylinder now has a bore of 4.040 inches, or a 2.02 inch radius. Plug that back into the equation and we get 45.89 cubic inches per cylinder or 367 cubic inches. Not much bigger.
However, you can buy a new crankshaft that will allow the engine to be much larger. For example, Eagle sells a stroker crank for the 360 that is 4.000 inches - almost a half inch more stroke per cylinder. Plugging that number into your standard-bore engine nets 50.26 cubic inches per cylinder or 402 cubic inches. However, stroker cranks sometimes require extra machine work such as notching the bottoms of the cylinders, since the extra length of the throws still has to fit inside the same space in the block. I found this page that details the buildup of a stroked 360, including prices for everything except machine work:
http://www.coopofdoom.net/stroker.htmlI agree with HK - if you want to start learning about engines, find a 318 and do a mild buildup. I'm 43, building my first engine (the 440 that was in it) and am sure that the power produced is going to scare the heck out of me the first time I get in it. And I'm a professional driver with over 25 years behind the wheel. It far better to learn with less power - you're less likely to get into trouble. I know, I probably sound just like your dad, but almost anyone on here will tell you the same thing.