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There's a problem I can't figure out in my homework. I can't really understand what it's asking. Maybe someone can help.

A meteor enters the Earth's atmosphere and burns up at a rate that, at each instant, is proportional to its surface area. Assuming that the meteor is always spherical, show that the radius decreases at a constant rate.

I think the problem is asking me either to show that $\frac{dr}{dt} = 0$ (which I don't know how to do) or that the relationship $\frac{dV}{dt} / \frac{dA}{dt}$ has no parameter $\frac{dr}{dt}$, which I've done, I think.. $\frac{dV}{dt} / \frac{dA}{dt} = \frac {r}{2}$

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I believe it is asking you to prove that $\frac{\text{d}r}{\text{d}t} = \text{constant}$. –  Aryabhata Mar 2 '11 at 7:39

1 Answer 1

up vote 4 down vote accepted

Use $\dfrac{dV}{dt}=kA$ to show that $\dfrac{dr}{dt}=l$, assuming that rate of burning is expressed in terms of volume.

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