If p is inversely proportional to the square of q, and p is 19 when q is 8, determine p when q is equal to 3
$19:8^2=64$
$p:3^2=9$
We are multiplying by $\frac{9}{64}$, and the inverse is $\frac{64}{9}$.
So $p=\boxed{\frac{1216}{9}}$.