Final answer:
The Moon cooled faster than Earth because it has far less mass and gravity, making it unable to retain an atmosphere, and its surface is quickly stripped of volatiles. Additionally, the giant impact hypothesis explains differences in composition and size that contribute to cooling rates. Hence, option b) is correct.
Step-by-step explanation:
The reason the Moon cooled much faster than Earth after their formations is primarily due to its smaller size and mass. With only one-eightieth the mass of Earth and about one-sixth Earth's surface gravity, the Moon's lower gravity made it much easier for it to lose any atmosphere it might have acquired, such as that temporarily contributed by impacting comets. This atmosphere would quickly be lost as gas molecules would freeze onto the surface or escape into space. Furthermore, the Moon's deficiency in volatiles—elements and compounds that evaporate at relatively low temperatures—also facilitated its more rapid cooling compared to Earth.
The giant impact hypothesis suggests that the Moon was formed from the debris of a collision between Earth and a Mars-sized object, further supporting the differences in composition that would lead to different cooling rates. While the Earth's larger volume contributed to its longer cooling process, the Moon's smaller size allowed it to cool and solidify more quickly. This difference in volume and the associated gravitational effects are the main reasons for the different cooling rates, rather than any notion of the Moon's interior being hollow or differences in oxygen levels.