问题
已知空间立体 $\Omega$ 的体密度为 $\rho(x, y, z)$, 且 $\rho(x, y, z)$ 在空间立体 $\Omega$ 上连续，则，该立体的质心坐标 $(\bar{x}, \bar{y}, \bar{z})$ 为多少？选项
[A]. $\bar{x}$ $=$ $\frac{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}{\iiint_{\Omega} x \rho(x, y, z) \mathrm{d} v}$, $\bar{y}$ $=$ $\frac{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}{\iiint_{\Omega} y \rho(x, y, z) \mathrm{d} v}$, $\bar{z}$ $=$ $\frac{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}{\iiint_{\Omega} z \rho(x, y, z) \mathrm{d} v}$[B]. $\bar{x}$ $=$ $\frac{\iiint_{\Omega} x \rho(x, y, z) \mathrm{d} v}{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}$, $\bar{y}$ $=$ $\frac{\iiint_{\Omega} y^{2} \rho(x, y, z) \mathrm{d} v}{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}$, $\bar{z}$ $=$ $\frac{\iiint_{\Omega} z^{2} \rho(x, y, z) \mathrm{d} v}{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}$
[C]. $\bar{x}$ $=$ $\frac{\iiint_{\Omega} x \rho(x, y, z) \mathrm{d} v}{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}$, $\bar{y}$ $=$ $\frac{\iiint_{\Omega} y \rho(x, y, z) \mathrm{d} v}{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}$, $\bar{z}$ $=$ $\frac{\iiint_{\Omega} z \rho(x, y, z) \mathrm{d} v}{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}$
[D]. $\bar{x}$ $=$ $\frac{\iiint_{\Omega} x \rho^{\prime}(x, y, z) \mathrm{d} v}{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}$, $\bar{y}$ $=$ $\frac{\iiint_{\Omega} y \rho^{\prime}(x, y, z) \mathrm{d} v}{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}$, $\bar{z}$ $=$ $\frac{\iiint_{\Omega} z \rho^{\prime}(x, y, z) \mathrm{d} v}{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}$
$\bar{x}$ $=$ $\frac{\iiint_{\Omega} x \rho(x, y, z) \mathrm{d} v}{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}$, $\bar{y}$ $=$ $\frac{\iiint_{\Omega} y \rho(x, y, z) \mathrm{d} v}{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}$, $\bar{z}$ $=$ $\frac{\iiint_{\Omega} z \rho(x, y, z) \mathrm{d} v}{\iiint_{\Omega} \rho(x, y, z) \mathrm{d} v}$