Question

One cubic centimeter of a typical cumulus cloud contains 60 water drops, which have a typical radius of 10 μm. (a) how many cubic meters of water are in a cylindrical cumulus cloud of height 3.2 km and radius 1.0 km

Answer 1

First calculate for the volume of the cylindrical cumulus cloud:

V = π r^2 h

V = π (1.0 km)^2 * 3.2 km

V = 3.2π km^3 = 10.05 km^3

 

We know that there are 60 water drops per cm^3. Therefore:

drops = 10.05 km^3 * (60 drop / cm^3) * (100,000 cm / km)^3

drops = 6.032 x 10^17 drops

 

Calculating for the volume of 1 drop:

Vdrop = (4π/3) r^3

Vdrop = (4π/3) * (10 x 10^-6 m)^3

Vdrop = 4.19 x 10^-15 m^3

 

Hence total volume of the drop is:

Vtotal drops = 6.032 x 10^17 drops * 4.19 x 10^-15 m^3 / drop

Vtotal drops = 2,526.68 m^3