I've got this problem:
The stem of a particular mushroom has a cylindrical shape. A stem with $2$ cm of height and $r$ centimeters of radius which has a volume $V=2 \pi r^2$. Use differentials to determine the approximated increase of the stem's volume where its radius grows from $0.4$cm to $0.5$cm.
So I got the $dr$ from the difference of $0.4 - 0.5$ which means its result was $0.1$. Right after that, $Dv=4 \pi r dr$. I calculated this without the value of $r$ and I think you can't do it that way, the result was $1.256r \ \text{cm}^3$ but I think there is something left.