The surface area $S$ of a sphere is directly proportional to the square of the radius $r$. 

1. Express $S$ as a function of $r$.

   Hint (a):

   Do not forget the constant of proportionality ($k$).

   Answer (a):

   $S\left(r\right) = kr^{2}$

2. Solve for the particular value of $k$ if the surface area is $16π \text{ cm}^{2}$ when the radius is $2$ cm. Then find the surface area when the radius is $3$ cm.

   Hint (b):

   Substitute the given point $\left(r,S\right)$ into your function in part (a) to find $k$.
   Then use the resulting equation to find the surface area when $r = 3$ cm.