A

Step 1: Understand the concept of heat transfer in solids. The rate at which an object cools is influenced by its surface area and its volume.

Step 2: Calculate the surface area for both the solid sphere and the hollow sphere:
- For the solid sphere, the surface area, $A_{solid} = 4 \pi R^2$.
- For the hollow sphere, the outer surface area, $A_{hollow} = 4 \pi R^2$, but it also has no heat capacity associated with the inner surface when it is hollow.

Step 3: Relate cooling to Newton's Law of Cooling which states that the rate of heat loss of a body is proportional to the difference in temperature between the body and its surroundings and its surface area.

Step 4: Compare heat capacities:
- The solid sphere has a greater mass and thus a higher heat capacity as compared to the hollow sphere with a smaller effective mass for the same outer radius. Therefore, it will retain heat for a longer period.

Step 5: Analyze the cooling process: The hollow sphere, made of the same material but with less volume, will cool faster than the solid sphere due to its less thermal inertia and higher surface area to volume ratio.

Therefore, the hollow sphere cools faster than the solid sphere.