\frac{\frac{1}{4} m + ρ_{v} (1 - β) \frac{1}{8} V}{\frac{1}{8} V} = ρ_{v} \Rightarrow \frac{2 m}{V} = β ρ_{v}

${\frac{\frac{1}{4}m + \rho_v(1 - \beta )\frac{1}{8}V}{\frac{1}{8}V} = \rho_v \quad\Rightarrow\quad \frac{2m}{V} = \beta \rho_v}$

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