(Solved): A sphere, centered at the origin, has radius 3 . Find integrals that compute its volume, using Car ...

A sphere, centered at the origin, has radius 3 . Find integrals that compute its volume, using Cartesian, cylindrical, and spherical coordinates. For your answers \( \theta= \) theta, \( \phi= \) phi, and \( \rho= \) rho. Cartesian \[ \int_{a}^{b} \int_{c}^{d} \int_{e}^{f} p(x, y, z) d z d x d y= \] \[ d z d x d y \] Cylindrical \[ \int_{a}^{b} \int_{c}^{d} \int_{e}^{f} f(r, \theta, z) d z d r d \theta= \] \( d z d r d \theta \) Spherical \[ \int_{a}^{b} \int_{c}^{d} \int_{e}^{f} g(\rho, \theta, \dot{\phi}) d \rho d \theta d \phi= \] \( d \rho d \theta d \phi \) Note: You can earn partial credit on this problem.