The height $\left(h\right)$ of a cylinder varies directly with the volume $\left(V\right)$ and inversely with the square of the radius of the base.

1. Find an equation for the height in terms of the volume and the radius. Use $k$ to represent the constant of proportionality.

   Answer (a):

   $h=\frac{kV}{r^{2}}$

2. When the volume is $20$ and the radius is $2$, the height is $15$. Find the height when the radius is $3$ and the volume is $10$.

   Answer (b):

   $h=\frac{10}{3}$