1-20 할리데이 10판 솔루션 일반물리학

$$ \begin{cases} \rho_{WATER} &= 1000\ut{kg/m^3} \\ 1\ut{gal} &= 231\ut{inch^3} \\ 1\ut{inch} &= 2.540\ut{cm} \\ v &= 1.5\ut{g/min} \end{cases} $$ (a) $$ \begin{aligned} \Ans &= 1000000\ut{cm^3} - 193\ut{gal} \\ &= 1000000\ut{cm^3} - 193\ut{gal}\cdot\frac{231\ut{inch^3}}{1\ut{gal}}\cdot\left(\frac{2.54\ut{cm}}{1\ut{inch}}\right)^3 \\ &= 1000000\ut{cm^3} - \frac{91323059289}{125000}\ut{cm^3} \\ &= \frac{33676940711}{125000}\ut{cm^3} \\ &= 269415.525688\ut{cm^3} \\ &\approx 269\ut{L} \end{aligned} $$ (b) $$ \begin{aligned} \Ans &= Time = \frac{Volume}{Speed} \\ &= \frac{193\ut{gal}}{1.5\ut{g/min}} \\ &= \frac{91323059289}{125000}\ut{cm^3} \cdot \frac{1\ut{min}}{1.5\ut{g}}\cdot \frac{1000\ut{g}}{1\ut{kg}}\cdot \frac{1000\ut{kg}}{1\ut{m^3}}\cdot \left(\frac{1\ut{m}}{100\ut{cm}}\right)^3 \\ &= \frac{30441019763}{62500}\ut{min} \\ &= 487056.316208\ut{min} \\ &\approx 8117.61 \ut{h} \\ &\approx 338.234 \ut{days} \\ &\approx 338 \ut{days} \end{aligned} $$