A sphere, centered at the origin, has radius $2.$ Find integrals that compute its volume, using Cartesian, cylindrical, and spherical coordinates. For your answers $=$ theta, $=$ phi, and $=$ rho.

Cartesian

Cylindrical

${\displaystyle \underset{a}{\overset{b}{}}}{\displaystyle \underset{c}{\overset{d}{}}}{\displaystyle \underset{e}{\overset{f}{}}}f(r,,z)dzdrd={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}dzdrd$

Spherical

${\displaystyle \underset{a}{\overset{b}{}}}{\displaystyle \underset{c}{\overset{d}{}}}{\displaystyle \underset{e}{\overset{f}{}}}g(,,)ddd={}_{}^{}ddd$