Equilibrium shapes of smectic-A domains in an isotropic phase formed on a substrate surface have been observed using a polarizing microscope. Polarizing-microscope images of some possible structures are simulated to determine the shape of the smectic-A domains. It is found from a comparison between experimental and simulated images that the shape formed on the substrate surface is a hemisphere. The hemispherical smectic-A domains are shown to be equilibrium shapes in terms of a theory proposed earlier (H. Naito, M. Okuda and Z. Ou-Yang, Phys. Rev. Lett. 70, 2912 (1993)) by taking account of the change in the transition temperature from an isotropic phase to a coexisting phase during the growth of a smectic-A phase.