Protons and neutrons, which are the two most common types of baryons, are indeed composed of three quarks each. Protons consist of two up quarks and one down quark, while neutrons consist of two down quarks and one up quark. These quarks are elementary particles and are considered to be point-like, meaning they do not have a defined size or shape.
The reason protons and neutrons are often described as spherical is because of the way the quarks are distributed within them. Quarks are held together by the strong nuclear force, which is mediated by particles called gluons. The gluons act as the "glue" that binds the quarks together.
Inside a proton or neutron, the quarks and gluons are in a state known as a "quark-gluon plasma." In this state, the quarks and gluons are constantly interacting and exchanging gluons. Due to these interactions, the distribution of quarks within the proton or neutron becomes diffuse, spreading out the charge and mass throughout the particle.
This diffuse distribution of quarks gives rise to an effective charge and mass distribution that appears approximately spherical when probed at certain scales. From experimental measurements, the charge distribution of a proton or neutron appears to be consistent with a roughly spherical shape.
However, it is important to note that the concept of "shape" at the subatomic level is not as straightforward as it is at the macroscopic level. Quarks are quantum mechanical particles, and their behavior is governed by the laws of quantum mechanics. They do not have well-defined positions or trajectories, and their properties are described by probability distributions.
In summary, while protons and neutrons are composed of three quarks, their spherical nature arises from the diffuse distribution of these quarks within the particles, as a result of the strong nuclear force interactions.