Consider a container of the shape obtained by revolving a segment of the parabola $x = 1 + y ^ { 2 }$ around the $y$-axis as shown below. The container is initially empty. Water is poured at a constant rate of $1 \mathrm {~cm} ^ { 3 } / \mathrm { s }$ into the container. Let $h ( t )$ be the height of water inside the container at time $t$. Find the time $t$ when the rate of change of $h ( t )$ is maximum.