Consider an axisymmetric container, initially filled with water to a depth $h_{I}$. A small circular hole of radius $r_{0}$ is opened in the base of the container at $z=0$.

(a) Determine how the radius $r$ of the container should vary with $z<h_{I}$ so that the depth of the water will decrease at a constant rate.

(b) For such a container, determine how the cross-sectional area $A$ of the free surface should decrease with time.

[You may assume that the flow rate through the opening is sufficiently small that Bernoulli's theorem for steady flows can be applied.]