91Ó°ÊÓ

Each water drop has a radius of \( r = 10 \mu m = 10 \times 10^{-6} \) meters. The volume \( V \) of a water drop can be calculated using the formula for the volume of a sphere: \[ V = \frac{4}{3} \pi r^3 \] Substituting \( r = 10 \times 10^{-6} \), we get: \[ V_d = \frac{4}{3} \pi (10 \times 10^{-6})^3 \approx 4.19 \times 10^{-15} \text{ m}^3 \] This is the volume of a single water drop.

The cylindrical cloud has a height (\( h \)) of \( 3 \text{ km} = 3000 \text{ m} \) and a radius (\( R \)) of \( 1 \text{ km} = 1000 \text{ m} \). The volume \( V_{cloud} \) of the cloud is given by: \[ V_{cloud} = \pi R^2 h = \pi (1000)^2 (3000) = 3\times10^9 \pi \text{ m}^3 \] Within the cloud, we have between 50 and 500 drops per cubic centimeter. Converting this to cubic meters, we have \( 5 \times 10^7 \) to \( 5 \times 10^8 \) drops per cubic meter. Calculate the total volume of water for this range: - For the lower range: \[ V_{total,low} = 3\times10^9 \pi \times 5 \times 10^7 \times 4.19 \times 10^{-15} \approx 197 \text{ m}^3 \]- For the higher range: \[ V_{total,high} = 3\times10^9 \pi \times 5 \times 10^8 \times 4.19 \times 10^{-15} \approx 1970 \text{ m}^3 \]

Since 1 cubic meter is equivalent to 1000 liters, we can convert the total volumes from cubic meters to liters.

Using the liters from above: - Lower range: 197 cubic meters \( \times 1000 \text{ liters/m}^3 = 197,000 \) liters - Higher range: 1970 cubic meters \( \times 1000 \text{ liters/m}^3 = 1,970,000 \) liters These are the numbers of 1-liter bottles that can be filled, respectively.

Water has a density \( \rho \) of \( 1000 \text{ kg/m}^3 \). The mass of water is therefore the volume times the density. For the lower range: \[ m_{low} = 197 \text{ m}^3 \times 1000 \text{ kg/m}^3 = 197,000 \text{ kg} \] For the higher range: \[ m_{high} = 1970 \text{ m}^3 \times 1000 \text{ kg/m}^3 = 1,970,000 \text{ kg} \] These are the mass values for the lower and higher range respectively.