| Surface | Rectangular | Cylindrical |
|---|---|---|
| (a) Half-Plane | \(y=x\tan k\) | \(\theta =k,\quad\) \(-\dfrac{\pi }{2}\lt k\lt\dfrac{\pi }{2}\) |
| (b) Plane | \(z=k\) | \(z=k\) |
| (c) Cylinder | \(x^{2}+y^{2}=a^{2}\) | \(r=a,\quad\) \(a\gt0\) |
| (d) Sphere | \(x^{2}+y^{2}+z^{2}=R^{2}\) | \(r^{2}+z^{2}=R^{2}\) |
| (e) Circular cone | \(x^{2}+y^{2}=a^{2}z^{2}\) | \(r=az,\quad a\gt 0\) |
| (f) Circular paraboloid | \(x^{2}+y^{2}=az\) | \(r^{2}=az,\quad\) \(a\gt0\) |