I have been working on some homework problems where I am asked to convert a standard equation of a surface into cylindrical and/or spherical. I understand the conversions for the most part but I struggle to understand how to find the range the variables such as $0<\theta<5$ or with the other variables $\rho, \phi$ and r. here is an example from my homework this case I will be using cylindrical the first octant portion of the cone $z=sqrt(x^2+y^2)/2$ between the planes z=0 and z=3 the resultant parametrization becomes $(r cos \theta)i +(r sin \theta)j + (r/2)k$ and according to my textbook the range of r and theta become $0 \le r \le 6$ and $0\le \theta \le \pi/2$ How do they get the range of r and theta
thanks for the help