Problem

Part I Multiple Choice

10. Consider the spherical coordinates system $x=\rho\sin\phi\cos\theta$, $y=\rho\sin\phi\sin\theta$, and $z=\rho\cos\phi$. The volume element $\mathrm{d}V=\mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z$ can be changed as

(A) $\rho\sin\phi\,\mathrm{d}\rho\,\mathrm{d}\theta\,\mathrm{d}\phi$.

(B) $\rho\cos\phi\,\mathrm{d}\rho\,\mathrm{d}\theta\,\mathrm{d}\phi$.

(C) $\rho^2\sin\phi\,\mathrm{d}\rho\,\mathrm{d}\theta\,\mathrm{d}\phi$.

(D) $\rho^2\cos\phi\,\mathrm{d}\rho\,\mathrm{d}\theta\,\mathrm{d}\phi$.