Answer
$S=kr^2\theta^2$
where k = constant of proportionality
Work Step by Step
RECALL:
(i)
If the quantities (or variables) $x$ and $y$ are related by the equation $y=kx$, then $y$ is directly proportional to $x$, where $k$ is the constant of proportionality.
(ii)
If the quantities (or variables) $x$ and $y$ are related by the equation $y=\dfrac{k}{x}$, then $y$ is inversely proportional to $x$, where $k$ is the constant of proportionality.
$S$ is given to be directly proportional to the product of $r^2$ and $\theta^2$ therefore the equation that expresses the given statement is:
$S = kr^2\theta^2$ where k = constant of proportionality