Question

One cubic centimeter of a typical cumulus cloud contains 50-500 water drops,which have a typical radius of 10 micro meter. For that range,give the lower higher value for the following. How many cubic meters of water are in a cylindrical cumulus cloud of height 3km radius1km? How many 1L bottles would the water fill? Water has a density of 1000kg/m³ . How much mass does the water in the cloud have ? Do not link it to any other question and give me the final answer to this question only.

Answer 1

$$\begin{gathered} 1c{m}^{3}ofthecloudhas50-500waterdrops. \\ andeachdropis10\mu m. \\ Volumeofonedrop=4/3\pi r^3 \\ =4/3\pi (10\times {10}^{-6}{)}^3=1.33\pi \times {10}^{-15}{m}^3 \\ Thecyclindricalcumulousofthecloud=\pi r^{2}h \\ =\pi (1000{)}^2\times 3 \\ =3\pi \times {10}^6{m}^3 \\ 1c{m}^3=({10}^{-2}{)}^3={10}^{-6}m \\ Numberofsuchsmallglubulesthatcanbeformedinacylinder=3\pi \times {10}^6/{10}^{-6} \\ =3\pi \times {10}^{12} \\ Nowtheminimumvolumeofraindropsinthiscomposition=50\times 3\pi \times {10}^{12}\times 1.33\pi \times {10}^{-15}=1.968m^3 \\ Maximum=500\times 3\pi \times {10}^{12}\times 1.33\pi \times {10}^{-15}=19.68m^3 \\ Now,1L=1m^3 \\ So,mimumwaterbottlesthatcanbestored=1.96approx2 \\ andmaximum=20bottles. \\ Themassofwater=Volume*density=1.968*1000=1968kgs \\ andlikewisemaximum=19680kgs. \end{gathered}$$