Problem $10.$ A clay cylinder is getting crushed in such a way that its radius is increasing while its height is decreasing. You may assume that it always remains a perfect cylinder, and that the total volume of clay is unchanging.

If the total volume of clay is $2c{m}^3,$ and the height is decreasing at a constant rate of $0\mathrm{.}1c\frac{m}{m}in,$ what is the rate of change of the radius when the height is $1$ cm $?$ Hint: the rate of change of the height is negative.