A spherical raindrop evaporates at a rate proportional to its surface area. Write a differential equation for the volume of the raindrop as a function of time.

How do I work this out.

Thanks
Henry

I'l try not to spoil your fun entirely by just giving away a solution.

I'm assuming you got as far as writing

Now, we know that $V=4\pi r^3/3$. See if you can find what $\mathrm{dV}/\mathrm{dt}$ is in terms of $\mathrm{dr}/\mathrm{dt}$ and $r$ (hint: use chain rule)...
Is this homework?

Brad

This isn't homework, its out of a degree level book. The book gives the answer as
dV/dt = -kV^2/3
which I can't make any sense out of.

Henry

Alright. First, the equation I gave above isn't entirely correct: We want instead

dV/dt=-Cr² (1)

(can you see why, with the constant of proportionality being C/(4pi )). Using that V=(ar)³ , for some constant a, which we could find, but don't really care about. Therefore, r=V^1/3 /a. Putting this into (1), we get that, for some new constant k=C/a² ,

dV/dt=-kV^2/3

Which is what we want.

I moved pretty fast there, so if you didn't follow something, just write back.

Brad

Thanks Brad. Thats insultingly easy!

Henry