设有空间区域 $\Omega_{1}: x^{2}+y^{2}+z^{2} \leqslant R^{2}, z \geqslant 0$; 及 $\Omega_{2}: x^{2}+y^{2}+z^{2} \leqslant R^{2}, x \geqslant 0, y \geqslant 0, z \geqslant 0$, 则( )
A. $\iiint_{\Omega_{1}} x \mathrm{~d} v=4 \iiint_{\Omega_{2}} x \mathrm{~d} v$.
B. $\iiint_{\Omega_{1}} y \mathrm{~d} v=4 \iiint_{\Omega_{2}} y \mathrm{~d} v$.
C. $\iiint_{\Omega_{1}} z \mathrm{~d} v=4 \iiint_{\Omega_{2}} z \mathrm{~d} v$.
D. $\iiint_{\Omega_{1}} x y z \mathrm{~d} v=4 \iiint_{\Omega_{2}} x y z \mathrm{~d} v$.