Answer
Circular cone with axis as the z-axis
$x^{2}+y^{2}=z^{2}$
Work Step by Step
Given: $r=\lt s cost, s sint, s\gt$
Write the vector equation in its equivalent parametric equations:
$x=s cost $, $y= s sint$ and $z=s$
Solving the first two parametric equations yields:
$x^{2}+y^{2}=s^{2}cos^{2}t+s^{2}sin^{2}t$
$x^{2}+y^{2}=s^{2}(cos^{2}t+sin^{2}t)=s^{2}(1)$
$x^{2}+y^{2}=s^{2}$
or
$x^{2}+y^{2}=z^{2}$
which represents as a equation of a circular cone with axis as the z-axis.
