An exoplanet has a surface area nine times larger than Earth.All other factors being equal,how would the exoplanet's cooling time compare to Earth's?
A) nine times shorter
B) three times shorter
C) three times longer
D) nine times longer

Question

Quizplus · Accepted Answer

The cooling time of a planet is proportional to its volume/surface area ratio. If the surface area is nine times larger, assuming the planets are similar in composition and density, the volume would increase by a factor of $3^3 = 27$ (since volume scales with the cube of the radius and surface area with the square). Therefore, the volume/surface area ratio increases, leading to a longer cooling time. However, the specific choice of "three times longer" accounts for the square-cube law, where increasing dimensions by a factor of 3 increases area by $3^2 = 9$ and volume by $3^3 = 27$, thus affecting the cooling rate.

An Exoplanet Has a Surface Area Nine Times Larger Than