Answer
$x =\dfrac{az}{h} \cos \theta; y=\dfrac{az}{h} \sin \theta$ and $z=Z$
Work Step by Step
Let us consider $Z$ be the axis parameter and the radial parameters can be written as: $\sin \theta$ and $\cos \theta$. Assume that $a$ be the radius of the base of the cone with height $h$.
Here, $\theta \in [0, 2\pi]$ and $0 \leq Z \leq h$.
Thus, the parametric description for a cone with radius $a$ and at the height $z$ of the cone can be expressed as:
$x =\dfrac{az}{h} \cos \theta; y=\dfrac{az}{h} \sin \theta$ and $z=Z$
