Solving Cloud Physics Problems - Brad's Request for Help

Therefore, the number of drops can be calculated using the equation: N = (3 * A * h) / (4 * pi * r^3)Where N is the number of drops, A is the area to be covered, h is the depth of rainfall, and r is the radius of each drop. In order to calculate N, we need to know the values of A, h, and r. The given values are A = 1 * 10^21, h = 0.5 cm, and r = 0.5 * 10^-4m. Plugging these values into the equation gives us:N = (3 * (1 * 10^21) * (0.5 cm

Hi I have those 2 problems:

A typical cloud contains droplets of water with an average radius of .5 * 10^-4m.
how many droplets are needed for a cloud that provides a rainfall of .5 cm.
( the answer must be 1*10^21 droplets)

for this second problem I don't know how to find two equations:

A force F acting on a body of mass m a distance r from some origin has a magnitude of F=(A*m*exp(h*r))/r^4, where A and h are both constants.
Given that the force has dimensions kilogram-meter per seconds squared, what are the dimensions of both A and h.

Please can I have some help or suggestions for those problems?

Thank you very much

(a) $$N = \frac{3 A h}{4 \pi r^3}$$

where A is the area to be covered, h = 0.5 cm is the depth and r is the radius of each drop.

(b) Hint: the argument of the exponential must be dimensionless - and - the dimensions of mA must be that of the force.

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Yeah (b) shouldn't be a problem...

But what is (a)??

Granted I'm in high school but I've never encountered that kind of physics... where does it come from?

It is college physics freshman
but I am sure U can do it

I have no idea how Tide find the solution for the first problem ( N=...)
I will try to work on it but if I don't find something I will ask him how he did it.
Thanks