Answer
a) $y= 8x^2$
b) $y= 72$
Work Step by Step
Since $y$ varies directly with $x^2$, we can write \begin{equation}
y= kx^2,
\end{equation} where $k$ is the constant of proportionality that must be determined.
a) Given that $y= 648$ when $x= 9$, we can use this information to find $k$ as follows: \begin{equation}
\begin{aligned}
648&= 9^2k\\
\frac{648}{81}&=k\\
\therefore k&=8.
\end{aligned}
\end{equation} The required model is
\begin{equation}
y= 8x^2.
\end{equation} b) Determine $y$ when $x=3$.
\begin{equation}
y= 8\cdot 3^2= 72.
\end{equation} The answer is $y= 72$ when $x= 3$.
