Why doesn't the violin have a large hollow body like the guitar?

The shape of the stringed instruments, such as violins consist of an upper bout, and two C shape bouts on either side. When looking at the front or back of the instrument, the features create an "hourglass" figure to the instrument. One purpose of the shape is that it's "waist" comes inward to give the bow easier access to the strings.

Like many bowed string instruments, the middle of the violin is convex, and C shaped so that the bow can easily play each string with a long sustain and no conflict with the shape. Also, the rounded top is so that the strings can be played both individually and one at a time. Violin makers knew that a more extended configuration would allow for greater depth while still being playable.