Proportionalities involving surface are and volume of a sphere.

**viet** · February 8th 2010, 01:47 PM

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?

not sure where to being, please help

**HallsofIvy** · February 9th 2010, 01:53 AM

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.

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