Intersection of a parametric equation and a plane

Question

Use $cos(t)$ and $sin(t)$, with positive coefficients, to parametrize the intersection of the surfaces $x^2+y^2=36$ and $z=6x^3$.

I have found $<6cos(t), 6sin(t)>$, but I haven't pined down $z$. I have tried $6(\sqrt{36-t^2})^3$ and $6(cos(t))^3$

Answer 1

Hint: What do get if you substitute $\ 6\cos\left(t\right)\ $ for $\ x\ $ in the equation $\ z=6 x^3\ $?