I am going to make a 4 string next and just making some inquiries to pad out my brain a little.  Does the Box size/dimensions affect the tone/volume of the end product?  How do changes in shape of the box change the sound?.  I am looking for a large cigar box and will end up with whatever I can get but I would like to know in advance if the box is worth buying or not.  Long and skinny with thin top?? square shape and deep?  does it really matter?

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General rule is .. more "volume" in size  = more "volume" in  sound .  Indeed,   size  and thickness effects  tone also . Most folks like to go for a thin top  for better results , ETC ... But these "rules" are more-so for acoustic  results .  If you are  going  more electric based   with a mag pickup ,then most of the above rules  don't matter much.   Some like to  try and find a happy medium for both acoustic  and electric ,.In that case the "rules" would still apply .

That being said ,  many other things effect the sound . including materials .  hardness of  them,  and nut and bridge   etc (harder is usually better )  ,   etc..etc ..

and Murphy's law will still  dictate  the end result .  but this will put the odds in your favor. 

 hope that helps 

 Very thorough comment from Pick, there. The only thing I can think to add is that sometimes the back is thinner than the top making it louder. And sometimes, the back looks better than the front. The Padron here is quite a bit smaller than my other two, but is just as loud. Part of it design differences I made, (the others have the embossed side on the string side), and part of it because it's thinner? I dunno for sure, but it's interesting. The back on this one was a lot prettier as well. 

Gitty has big boxes that are made for cbg’s, they come unfinished, so you can do anything to them?

Hi Donald, the answers above pretty well give the full picture. However, not mentioned is the soundhole/s [size and positioning] that also play an important role in sound creation as does the bridge, its positioning and height.
I have found that a bigger sound box may not always equate to better volume but will vary the tone and as also already mentioned the materials used play a large part in the quality of the sound.

As an example, the smaller guitar pictured here is noticeable louder than the one on the right. However, the larger guitar, as you would expect, has a deeper tone.
I have included a list of things that I take into consideration when designing a guitar.

As the sound we hear is created by the vibration of the top [exited by the strings] moving the air in the box, in the form of sound waves, so the larger the area under the bridge would be better, as opposed to a long narrow box. If one looks at regular guitars and most other stringed instruments, their bridges are at the widest part of the body. Talking acoustic guitars of course.
Cheers Taff

I agree that volume generally gives more sound. The Sound hole needs to be big enough but after that bigger doesn't help. you just need to get air flow. Removing material gives less for generating sound. On through necks I try to place a hole on each side. The biggest factor for me is sticking to a long scale length. Whenever I have reduced it significantly my tone and volume suffered. I stick to a 24.5 scale length. This about an inch shorter than a Fender. This is due to free material I get for necks. I used to try to adjust the length based on the size of the box, but gave it up, if it looks a little too long and plays better, so what? Sticking to a standard scale also speeds up the process. I have more than halved my build time due to this. I am not an expert builder and a terrible musician but this has been my take on it.

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