Mathematics

Problem

A right circular cylinder changes shape while keeping its volume constant at

100\,\text{cm}^3

. The radius

r(t)

and height

h(t)

satisfy

\pi r^2 h = 100

. At an instant when

r = 2\,\text{cm}

and

\displaystyle \frac{dr}{dt} = -0.05\,\text{cm/s}

, calculate

\displaystyle \frac{dh}{dt}

at that instant (include units).