For precipitation to form, cloud droplets must grow in volume by roughly times.

The correct answer is by roughly one million times.  

Any product of the condensation of atmospheric water vapor, which falls under gravity is known as precipitation. The main forms of precipitation are rain, drizzle, snow, sleet, and others.  

All the precipitation give rise to clouds and the clouds are produced when water vapor in the atmosphere condenses and cools. With the condensation of water vapor, the formation of water droplets takes place, and if the formation of clouds takes place within or is moved into the part of the atmosphere, which is below freezing then the droplets turn into ice crystals.  

In order to form precipitation, the cloud droplets must grow in volume by roughly one million times.  

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s