Question

One cubic centimeter of a typical cumulus cloud contains 400 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 0.9 km? (b) How many 1-liter pop bottles would that water fill? (c) Water has a density of 1000 kg/m3. How much mass does the water in the cloud have?

Answer 1

Answer:

A) 13.6 million cubic meters

B) 13.6 billion 1 liter pop bottles

C) 13.6 billion kg of water

Explanation:

A cubic centimeter of the cloud has 400 drops of water, so the volume of water contained is 400*Vdrop

The volume of a spheric drop of radius 10 um is:

$Vdrop = \frac{4}{3} \pi * r^3 = \frac{4}{3}\pi*(0.001 cm)^2 = 4.19e-6 cm^3$

So, 1 cm3 of this cloud contains 1.67e-3 cm3 of water.

This gives us a volume ratio of 1.67e-3.

If the cloud has a cylindrical shape with a height of 3.2 km and a radius of 0.9 km the total volume will be:

$V = h * \pi * r^2$

$V = 3.2 * \pi * 0.9^2 = 8.14 km^3$

And the content of water is

Vwater = vr * V = 1.67e-3 * 8.14 = 0.0136 km3 = 13600000 m3

A cubic meter contains 1000 liters, so the water from this cloud could fill 13.6 billion 1 liter pop bottles.

The mass is density*volume, so the mass of water in the cloud is of 13.6 billion kg.