Solving a Cumulus Cloud Math Problem: Lower & Higher Values

[theskyiscrape]

Homework Statement

one cubic centimeter of a typical cumulus cloud contains 50 to 500 water drops, which have a typical radius of 10 micrometers. for that range, give the lower and higher value, respectively, for the following. a) how many cubic meters of water are in a cylindrical cumulus cloud of height 3.0 km and radius 1.0 km? b) how many 1 liter pop bottles would that water fill? c) water has a density of 1000 kg/m^3. how much mass does the water in the cloud have?

Homework Equations

standard conversion factors and density (D=m/v)?

The Attempt at a Solution

not sure where to start on this one! this book has some really goofy ways of presenting problems and no answers in the back of the book so i never know if i am right or not. any help would be great! i am going to work on the other 20 homework questions i have to do by friday...

 

[AvroArrow]

a) Lower value: 2.5 x 10^9 m^3, Higher value: 2.5 x 10^10 m^3b) Lower value: 2.5 x 10^7 1-L bottles, Higher value: 2.5 x 10^8 1-L bottlesc) Lower value: 2.5 x 10^12 kg, Higher value: 2.5 x 10^13 kg

 

[kerimek]

As a scientist, it is important to approach problems systematically and use appropriate equations and conversion factors. Let's start by breaking down the problem into smaller parts and identifying the necessary information.

a) We are given the height and radius of the cloud, and we need to find the volume of water in the cloud. We can use the formula for the volume of a cylinder, V=πr^2h, where r is the radius, h is the height, and π is a constant. However, we need to convert the given values to meters, since the volume will be in cubic meters. So, the height would be 3000 m and the radius would be 1000 m. Plugging these values into the formula, we get V=π(1000 m)^2(3000 m) = 3 x 10^9 m^3. This is the total volume of water in the cloud.

b) To find the number of 1 liter pop bottles that the water would fill, we need to convert the volume from cubic meters to liters. Since 1 m^3 = 1000 liters, the volume in liters would be 3 x 10^9 x 1000 = 3 x 10^12 liters. Dividing this by 1 liter, we get 3 x 10^12 bottles of water.

c) To find the mass of the water in the cloud, we can use the density formula, D=m/v, where D is the density, m is the mass, and v is the volume. We are given the density of water as 1000 kg/m^3, and we found the volume in part a to be 3 x 10^9 m^3. Plugging these values into the formula, we get m=1000 kg/m^3 x 3 x 10^9 m^3 = 3 x 10^12 kg. This is the total mass of water in the cloud.

In summary, the lower and higher values for the given range are 50 and 500 water drops per cubic centimeter, respectively. The volume of water in the cloud is 3 x 10^9 m^3, which is equivalent to 3 x 10^12 liters or 3 x 10^12 1 liter pop bottles. The mass of the water is 3 x 10^12 kg. It is important to always