Rutherford's gold foil experiment allowed other deductions besides the nucleus occupying a small volume. But the deduction of the small volume is this: Most alpha particles hit nothing which meant that the atom consists mostly of space. A VERY FEW alpha particles (which are positively charged) were deflected at some angle and even FEWER were repelled (turned back on themselves). So wherever the positive charges were most alpha particles didn't come close to them. The fact that some alpha particles were actually repelled made a convincing story that the positive charge was concentrated in one place which Rutherford chose to call the nucleus AND that it occupied a very small volume compared to the atom as a whole.
Thank you :)