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, how does the amount of internal heat the Moon has compare to that of Earth?
A) The Moon's heating rate is 1/64 times that of Earth's.
B) The Moon's heating rate is 32 times that of Earth's.
C) The Moon's heating rate is 1/16 times that of Earth's.
D) The heating rates are about the same.
E) The Moon's heating rate is 8 times that of Earth's.

Question

Quizplus · Accepted Answer

The volume of a sphere is proportional to the cube of its diameter. Since the Moon's diameter is 1/4 of Earth's, its volume is (1/4)^3 = 1/64 of Earth's. Thus, the Moon's heating rate is 1/64 times that of Earth's.

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