Both protons and mesons are composed of quarks (3 in a proton, 2 in a meson), so that makes them lumpy, not spherical. How do you measure the radius of a lump?
At that scale of distance you can't talk about the location of a quark but only the probability of its being in any given location. The probability distribution of quarks in a proton in its ground state is spherical.
ask Victoria’s Secret?