Proportionalities involving surface are and volume of a sphere.

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February 8th 2010, 01:47 PM
viet

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?

not sure where to being, please help
February 9th 2010, 01:53 AM
HallsofIvy

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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