Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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.. $\frac{dV}{dt} / \frac{dA}{dt} = \frac {r}{2}$

share|cite|improve this question
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
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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.