If you have a parametrization of the surface of revolution generated by revolving the function $\displaystyle y=x^3$, and $\displaystyle 1\leq x\leq 2$ around the $\displaystyle x$-axis such that

$\displaystyle x=t$

$\displaystyle y=r(t)cos(\theta)$

$\displaystyle z=r(t)sin(\theta)$

How do you find $\displaystyle r(t)$ ?