Having a little trouble with an optimization question:
A half-spherical raindrop of diameter 1cm is sitting on a picnic table. It is evaporating
at a rate of 1cm^3 per 10 min. How fast is the rop's circular footprint shrinking when
the diameter is half its original width?
So what I think needs to be found is $\dfrac{\mathrm{d}D}{\mathrm{d}t}$ and I know that the volume of a half sphere is $\dfrac{4 \pi r^3}{6}$.
So what I have to do is differentiate the equation and then half it...? How do I do this?