1-24 할리데이 10판 솔루션 일반물리학

$$ \begin{cases} R &= 60\ut{\mu m} \\ \rho_{\text{SiO}_2} &= 2600\ut{kg/m^3} \\ L &= 1.00\ut{m} \end{cases} $$ $$ \begin{aligned} \\ n\cdot S_{\text{particle}} &= S_{\text{cube}} \\ n &= \frac{S_{\text{cube}}}{S_{\text{particle}}} \end{aligned} $$ $$ \begin{aligned} \\ \Ans &= \Sigma m = nm =n\rho V_{\text{particle}} \\ &= \frac{S_{\text{cube}}}{S_{\text{particle}}}\rho V_{\text{particle}} \\ &= \frac{S_{\text{cube}}}{4\pi R^2}\rho (\frac{4}{3}\pi R^3) \\ &= \frac{S_{\text{cube}}\rho4\pi R^3}{4\pi R^2\cdot3} \\ &= \frac{S_{\text{cube}}\rho R}{3} \\ &= \frac{6\ut{m^2}\cdot 2600\ut{kg/m^3}\cdot 60\ut{\mu m}}{3} \cdot \frac{1\ut{m}}{10^6\ut{\mu m}} \\ &= \frac{39}{125}\ut{kg} \\ &= 0.312\ut{kg} = 312\ut{g} \end{aligned} $$