(Solved): 5. Identify the surfaces in spherical coordinates. \[ S_{1}: \rho \sin \phi=1, \quad S_{2}: \rho \ ...

5. Identify the surfaces in spherical coordinates. \[ S_{1}: \rho \sin \phi=1, \quad S_{2}: \rho \cos \phi=2, \quad S_{3}: \phi=\frac{\pi}{6} \] a. \( S_{1} \) : cylinder, \( S_{2} \) : horizontal plane, \( S_{3} \) : cone b. \( S_{1} \) : horizontal plane, \( S_{2} \) : cylinder, \( S_{3} \) : cone c. \( S_{1}: \) sphere, \( S_{2}: \) cylinder, \( S_{3} \) : vertical plane d. \( S_{1}: \) cone, \( S_{2}: \) sphere, \( S_{3} \) : vertical plane e. \( S_{1} \) : sphere, \( S_{2} \) : horizontal plane, \( S_{3} \) : cylinder