Molecular dynamics (MD) simulations of nanodroplets containing water and nonane show them to be nonspherical and strongly phase separated. A simple, but realistic model for these "Russian doll" structures is a spherical nonane lens that partially wets a spherical water droplet. This document contains an analytical calculation of the particle form factor P(q) needed to analyze experimental measurements of small angle neutron and x-ray scattering from aerosols of particles with this type of structure. In addition, an exact formulation of the particle form factor is developed for cylindrically symmetric droplets with otherwise arbitrary scattering length density functions. This result will be useful to calculate P(q) directly from MD simulation results. We compare results using both formulations and find excellent agreement between them.