One cubic centimeter of a typical cumulus cloud contains 50 to 500 water drops, which have a typical radius of

Question

10 nanometers. How many cubic meters of water are in a cylindrical cumulus cloud of height 3 km and radius 1 km? (using 50 first and then 500)

Answer 1

A cylindrical cloud of height 3km and radius 1km has a total volume of:

V = pi * R² * h.

Converting the numbers to centimeters (3 km = 300,000 cm, 1 km = 100,000 cm), I get a value of:

V = 9.24 * 10^15 cm^3.

So, the cloud holds 9.24 * 10^15 cubic centimeters.

- How many drops does it hold? (multiply by 50 or 500 as appropriate.)

- What is the volume, in m^3, of a drop? (The drops are spheres, with volume (4 pi / 3) r³.)

Multiply those two numbers by each other to get the total volume of water in the cloud.

Answer 2

I got 9.42477 x 10↑15 cubic centimeters. or 9.42 instead of 9.24

9.42 x 10↑15 x 50 = 4.71 x 10↑17 drops at 50 drops per cc

and 4.71 x 10↑18 drops at 500 drops per cc.

By the way, you must also remember that the drops are sperical and therefore must find the volume of a sphere with a .000000010 meter diameter, then multiply that times the number of drops we obtained above.

If I remember correctly the volume of a sphere is 4/3 Π  r↑3

______________________________________...

Π = pi = 3.1415926535897932384626433832795...+

but for most common calculations is taken as 3.1416  or even 3.14

4/3 x 3.1416 = 4.1888

or

4/3 x 3.14 ≈ 4.19