1. ## evaporation rate

this question is giving me a really hard time...

A spherical drop of radius r(t), r cms, t minutes evaporates at a rate proportional to its surface area. Given that the volume v(t)=4/3╥r^(3) and the surface area s(t)=4╥r^(2), write down an ODE for r(t).

I am very stuck i have no idea of where to begin, can anyone please help me, Thank you

2. Originally Posted by acosta0809
r cms, t minutes evaporates at a rate proportional to its surface area. Given that the volume v(t)=4/3╥r^(3) and the surface area s(t)=4╥r^(2), write down an ODE for r(t).
I'll take a punt,

$\frac{dr}{dt} \propto 4\pi r^2 \implies \frac{dr}{dt} =k\times 4\pi r^2$

Now separating

$\frac{dr}{r^2} =k\times 4\pi~dt$

Can you solve this?