The Moon has a diameter that is approximately one-fourth that of Earth. If these objects' interiors are heated by radioactive decays, and the total amount of energy in decays is proportional to the object's volume, then how does the amount of heat the Moon has compare to that of Earth?
A) The Moon has 0.016 times that of Earth's.
B) The Moon's heating rate is 8 times that of the Earth's.
C) The Moon's heating rate is 0.5 times that of Earth's.
D) The Moon's heating rate is 4 times that of the Earth's.
E) The heating rates are about the same.

Question

Quizplus · Accepted Answer

The energy in decays is proportional to volume. Since the Moon's diameter is one-fourth that of Earth's, its volume is 1/64 of Earth's volume (since volume scales as diameter cubed). Therefore, if the energy from decays is proportional to the object's volume, then the Moon's heating rate is 1/64 that of Earth's. In other words, the Moon has 0.016 times the heating rate of Earth. So the answer is A).

The Moon Has a Diameter That Is Approximately One-Fourth That