# Math Help - Proportionalities involving surface are and volume of a sphere.

1. ## Proportionalities involving surface are and volume of a sphere.

the rate at which heat escapes from a planet is proportional to its surface area; $4 \pi R^2$. The amount of heat stored during the formation of a planet is proportional to its volume; $\frac{4 \pi R^3}{3}$. The radius R of Earth is twice of Mars. It takes Earth 5 billion years to lose all of its original heart of formation. How long will it take Mars to do so?

2. time to lose all heat is directly proportional to $R^3$ and inversely proportional to $R^2$ so is proportional to $\frac{R^3}{R^2}= R$. Since mars is half the radius of the earth, it will take 1/2 the time to cool.