The relationship you described is a direct variation, which can be written as:

$S = k \cdot p \cdot q$

Where $k$ is the constant of proportionality, and $S$, $p$, and $q$ are the given variables.

To find $k$, substitute the values of $S = 54$, $p = 6$, and $q = 2$ into the equation:

$54 = k \cdot 6 \cdot 2$

Simplifying:

$54 = k \cdot 12$

Now, solve for $k$:

$k = \frac{54}{12} = 4.5$

So, the constant of proportionality is $k = 4.5$.

Would you like further details or have any questions?

Here are 5 related questions:

1. If $S$ varies directly as $p$ and $q$, how would $S$ change if both $p$ and $q$ double?
2. Given $S = k \cdot p \cdot q$, how would you express $p$ in terms of $S$, $k$, and $q$?
3. If $S = 100$, $p = 8$, and $q = 3$, find the new value of $k$.
4. If the constant of proportionality is $k = 5$, and $p = 7$, $q = 2$, find $S$.
5. Can you explain the difference between direct variation and inverse variation?

Tip: Always double-check units when working with proportional relationships to ensure consistency throughout your calculations.