MEI Differential Equations Question

The radius of a circular ink blot is increasing at a rate inversely proportional to its area A. Find an expression for dA/dt.

So
dr/dt = k/A

A= pir^2
dA/dr = 2pi(r)

Then what? Are we supposed to use the chain rule? Becuase I tried that and it doesn't work, the answer in the back says-
k'/rootA

HELP!!

you've got

$\displaystyle \frac{dr}{dt} = \frac{k}{A}$

$\displaystyle A= \pi r^2$

$\displaystyle \frac{dA}{dr} = 2\pi r$

so $\displaystyle \frac{dr}{dt} \frac{dA}{dr} = \frac{dA}{dt} = \frac{2k}{r}$

but $\displaystyle A= \pi r^2$ so $\displaystyle \sqrt{\frac{A}{\pi}}= r$

see what you can do from there

Ahh thank you, I wasn't getting the answer stated by the book.

However, why is answer $\frac{2k\sqrt{\pi}}{\sqrt{A}}$ better than $\frac{2k}{r}$ ?