How loud an instrument sounds is not determined by its size. It's determined by the amount of coupling between the string (or whatever is generating the tone) and the air around the instrument.
Compare an acoustic guitar with an electric guitar: They are both of the same size, they both may use exactly the same strings (though they prefer different gauges). But one is loud enough to sing along (the acoustic guitar) while the other can hardly be heard unless you plug it into an amp. The difference? The electric guitar is basically a solid slap of wood that's purposefully way too heavy to vibrate significantly. As such, the vibration energy stays in the strings for a longer time, giving the instrument a much longer sustained sound than the acoustic guitar does. The acoustic guitar, by contrast, is built such that the thin planks of wood vibrate along with the strings, so that the vibrations can actually be turned into sound waves efficiently. The acoustic guitar has a much, much higher coupling between the strings and the surrounding air than the electric guitar.
Of course, this coupling is a continuous scale. You can find guitars that are louder (stronger coupling), and you can find violins that are quieter (weaker coupling) than other instruments of the same sort. But the violin has seen very intensive use as an orchestra instrument where a certain amount of volume is a must. And a strong coupling is not a problem for a violin because energy is constantly being supplied by the bow: There is no need to sustain a sound for a while. The guitar, on the other hand, is a plucked instrument, and as such the amount of available energy is fixed. The longer a note sounds, the quieter it gets. And the stronger the coupling is, the quicker the note will fade away. Which is not what most guitarists want: When they were able to reduce the coupling by relying on electric amplification instead, they almost immediately reduced the coupling to effectively zero in order to get a good, long sustain.