A cubic centimeter in a typical cumulus cloud contains 50 to 500water drops, whi

Question

A cubic centimeter in a typical cumulus cloud contains 50 to 500water drops, which have a typical radius of 10 µm. For thatrange, give the lower value and the higher value, respectively, forthe following. (a) How many cubic meters of water are in acylindrical cumulus cloud of height 3.6 kmand radius 1.2 km?
1 to 2m3

(b) How many 1 liter pop bottles would that water fill?
3 to 4bottles

(c) Water has a mass per unit volume (or density) of 1000kg/m3. How much mass does the water in the cloudhave?
5 to 6kg (a) How many cubic meters of water are in acylindrical cumulus cloud of height 3.6 kmand radius 1.2 km?
1 to 2m3

(b) How many 1 liter pop bottles would that water fill?
3 to 4bottles

(c) Water has a mass per unit volume (or density) of 1000kg/m3. How much mass does the water in the cloudhave?
5 to 6kg

Explanation / Answer

a) The volume of the cumulus cloud is equal to V =R2h = (1200m)2(3600m) = 1.6 x1010 m3. Since 1m3 =106 cm3, this is the same as 1.6 x1016 cm3. Since there are 50 to 500water droplets per cubic centimeter, there are anywhere from 1.6 x1016 * 500 = 8.1 x 1017 droplets to 1.6x 1017 * 500 = 8.1 x 1018 droplets. Thevolume of a single droplet can be found by using the formula V =4R3/3 = 4(10 x 10-6m)3/3 = 4.2 x 10-15 m3. Multiplying this by the range of droplets gives that there isanywhere from 3400 m3 of water to 34000 m3 ofwater. b) 1 L = 1000 mL = 1000 cm3 = 1000 x10-6 m3 = 10-3m3. So we can just divide the range of volumes bythis value to get the number of bottles than can be filled. The fewest number of bottles that could be filled is(3400m3)/(10-3 m3) = 3,400,000bottles, and the most that could be filled is(34000m3)/(10-3 m3) = 34,000,000bottles. c) We can multiply the density by the range in volumesobtained in part (a) to get the mass is somewhere from 3,400,000 kgto 34,000,000 kg. So, to recap: 1) 3,400 m3 water 2) 34,000 m3 water 3) 3,400,000 bottles 4) 34,000,000 bottles 5) 3,400,000 kg water 6) 34,000,000 kg water Note: Please do not bump your post. It makes peoplethink that people have already answered your question (because theysee it has already been responded to) So, in order to make itmore easily seen as an unanswered question, do not bump yourpost.

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