Question

A cylindrical tank has a radius of 3m and a depth of 10m. It is being filled at a rate of 5m^3/min. How fast is the surface rising?

Answer 1

\[
V=\pi r^2h\\
\frac{dV}{dt}=\pi r^2\frac{dh}{dt}\\
5=9\pi\frac{dh}{dt}\\
\frac{dh}{dt}=\frac5{9\pi}
\]