Meters of water are in a cylindrical cumulus cloud

[bilalbajwa]

Please help me!

Homework Statement

A cubic centimeter in a typical cumulus cloud contains 50 to 500 water drops, which have a typical radius of 10 µm. For that range, give the lower value and the higher value, respectively, for the following.
(a) How many cubic meters of water are in a cylindrical cumulus cloud of height 3 km and radius 1 km?

The Attempt at a Solution

Vdrop = 4/3 * pi * (10^-6 m)^3 = 4.189(10^-15) m^3

Vdrop*50 = (4.189(10^-15) m^3)*50=2.094*10^-13m^3---volume of water in a cubic centimeter of lumus cloud
Vdrop*500 = (4.189(10^-15) m^3)*500=2.094*10^-12m^3---volume of water in a cubic centimeter of lumus cloud

Vcloud = pi * 3(10^3) m * (1(10^3) m)^2 = (9.42*10^9) m^3

Lower value = 0.000001 m^3 volume can hold 2.094*10^-13m^3 vol of water
(9.42*10^9) m^3 volume can hold [(2.094*10^-13m^3)/0.000001 ]*((9.42*10^9) m^3) IS THIS RIGHT?

 

[Dick]

Yes, that's right. Why do you doubt it?

 

[m2003]

Higher value = 0.000001 m^3 volume can hold 2.094*10^-12m^3 vol of water
(9.42*10^9) m^3 volume can hold [(2.094*10^-12m^3)/0.000001 ]*((9.42*10^9) m^3) IS THIS RIGHT?

First, let's calculate the volume of water in a single cubic centimeter of a cumulus cloud. We can use the given information about the number of water drops and their radius to find that the volume of each drop is approximately 4.189 x 10^-15 cubic meters. Multiplying this by the lower and higher values of 50 and 500, respectively, we get a range of 2.094 x 10^-13 to 2.094 x 10^-12 cubic meters of water in a single cubic centimeter of a cumulus cloud.

Next, we can use the given height and radius of the cloud to calculate its volume. Using the formula for the volume of a cylinder, we find that the cloud has a volume of approximately 9.42 x 10^9 cubic meters.

To determine how many cubic meters of water are in the cloud, we can multiply the volume of a single cubic centimeter of water by the number of cubic centimeters in the cloud's volume. This gives us a range of 1.975 x 10^7 to 1.975 x 10^8 cubic meters of water in the cloud.

I hope this helps! It's important to remember to use the correct units and to double check your calculations to ensure accuracy. Keep up the good work!