Physics

The key is recognizing that cooling rate depends on the surface area available for heat loss, not the mass or volume. Both spheres radiate heat from their outer surfaces according to Newton's law of cooling—the rate is proportional to the exposed surface area. Since the solid sphere has outer surface $4\pi R^2$ and the hollow sphere has outer surface $4\pi A^2$, whichever has the larger outer radius will cool more slowly. The one with the smaller outer surface area will lose heat faster initially and therefore cool faster.

The key is recognizing that cooling rate depends on the surface area available for heat loss, not the mass or volume. Both spheres radiate heat from their outer surfaces according to Newton's law of cooling—the rate is proportional to the exposed surface area. Since the solid sphere has outer surface $4\pi R^2$ and the hollow sphere has outer surface $4\pi A^2$, whichever has the larger outer radius will cool more slowly. The one with the smaller outer surface area will lose heat faster initially and therefore cool faster.