In spherical coordinates the integral

${\displaystyle \underset{-4}{\overset{0}{}}}{\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{16-x^2}}{}}}{\displaystyle \underset{0}{\overset{\sqrt[\phantom{2}]{16-x^2-y^2}}{}}}f(x,y,z)dzdydx$

is equal to which of the following?

A$.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}{\displaystyle \underset{-\frac{}{2}}{\overset{\frac{}{2}}{}}}{\displaystyle \underset{0}{\overset{16}{}}}f(sincos,sinsin,cos){}^{2}sinddd$

B$.{\displaystyle \underset{0}{\overset{}{}}}{\displaystyle \underset{\frac{}{2}}{\overset{}{}}}{\displaystyle \underset{0}{\overset{4}{}}}f(sincos,sinsin,cos){}^{2}sinddd$

C$.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}{\displaystyle \underset{0}{\overset{}{}}}{\displaystyle \underset{0}{\overset{16}{}}}f(sincos,sinsin,cos){}^{2}sinddd$

D$.{\displaystyle \underset{0}{\overset{}{}}}{\displaystyle \underset{0}{\overset{2}{}}}{\displaystyle \underset{0}{\overset{4}{}}}f(sincos,sinsin,cos){}^{2}sinddd$

E$.{\displaystyle \underset{0}{\overset{\frac{}{2}}{}}}{\displaystyle \underset{\frac{}{2}}{\overset{}{}}}{\displaystyle \underset{0}{\overset{4}{}}}f(sincos,sinsin,cos){}^{2}sinddd$