Question

The droplet number concentration of a cloud is 100 per cm^3. What is the approximate distance between the centers of these droplets?

Answer 1

I'm really bad with spheres and such, so bear with me

Answer 2

I like bears, especially pandas :D

Answer 3

Oh and assume these droplets are uniformly dispersed

Answer 4

Assuming the 100 droplets completely takes up 1 cm^3 (which in reality it cannot) you can compute the volume of 1 droplet and then the radius. The approximate average distance between the two droplets will be 2*r.

Answer 5

I have the radius of each droplet, but I think we're assuming that these droplets are points rather than spheres with a certain volume for this part of the question.

Answer 6

If you assume they are spheres and compute 2*r are you not getting the correct answer?

Answer 7

Assuming they are spheres I am getting 0.1336 cm as the radius and 0.2673 cm as the approximate distance between two droplets.

What are your answer choices?

Answer 8

If you don't want to assume they are spheres, then another method is to assume a cube with side 1cm each. The volume of this cube is 1 cm^3. This holds 100 droplets. You can take the cube root of 100 which is 4.6416 and assume that many droplets are along each side so there will be a total of 4.6416 x 4.6416 x 4.6416 (=100) droplets in the entire cube. Now each side of the cube is 1 cm long and is occupied by 4.6416 droplets. Therefore, the average distance between the droplets is 1 / 4.6416 = 0.2154 cm.

Answer 9

Thanks, the first explanation was sufficient for this problem, but the second one involving the cube taught me a little bit about geometry so thank you for that too.

Answer 10

You are welcome.