How do you calculate the weight of a cloud?

Question

When you are given the number of drops per cubic centimeter (2000), the uniform size of the droplets (10 micrometers in diameter), and the dimensions of the cloud (1.kkm x 4 km x 1km)?

Answer 1

density.

density of water = 1 g/mL

Answer 2

2000 drops/cm^3 = 2 x 10^18 drops/km^3
10 micrometers = 1 x 10^-5 meters= 1 x 10^-8 km
1km x 4km x 1km = volume of 4 km^3

(2 x 10^18 drops/km^3) x (4 km^3) = number of drops in the volume
=8 x 10^18 drops

volume of a drop = 4/3(pi)(10^-8/2)^3=5.2 x 10^-25 km^3

8 x 10^18 drops x 5.2 x 10^-25 km^3 = volume of all the drops
4.16 x 10^-6 km^3

then convert back to cubic centimeters
4.16 x 10^9 cm^3

because 1 g/mL is the density of water and 1 ml = 1 cm^3
4.16 x 10^9 cm^3 = 4.16 x 10^9 g

that gives you mass and by W=mg you can find weight
(4.16 x 10^9 g) x (9.8 m/s^2) = 4.08 x 10^10 N

I might have made some conversion errors or something. It'll be best if you looked over it also.

Answer 3

The radius of a drop is
R = 5 * 10^-6 m

The volume of a drop is
v = 4/3*pi*R^3
v = 4/3*pi*(5 * 10^-6 m)^3
v = 5.24 * 10^-16 m^3

The volume of water in a cubic centimeter is
vcc = 2000*v
vcc = 2000*(5.24 * 10^-16 m^3)
vcc = 1.05 * 10^-12 m^3

The weight of water in a cubic centimeter is
w = rho*g*vcc
w = (1000 kg/m^3)*(9.81 m/s^2)*(1.05 * 10^-12 m^3)
w = 1.03 * 10^-8 N
where rho = density of water, and g = gravity

The number of cubic centimeters in the cloud is
n = (1 km)*(4 km)*(1 km) / (1 cm^3)
n = 4 * 10^15

The weight of the entire cloud is then
W = w*n
W = (1.03 * 10^-8 N)*(4 * 10^15)
W = 4.11 * 10^7 N

So, the cloud weighs about 4.11 * 10^7 Newtons (9.24 * 10^6 pounds).