Answer
$z^3=\frac{8}{97}(x^2+y^2)$
Work Step by Step
Step 1. Write the general form as $z^3=k(x^2+y^2)$ where $k$ is a constant.
Step 2. Use the given condition, $2^3=k(9^2+4^2)$, thus $k=\frac{8}{97}$
Step 3. We have $z^3=\frac{8}{97}(x^2+y^2)$
