#### Question

Just as precise measurements are necessary in science, it is equally important to be able to make rough estimates of quantities using rudimentary ideas and common observations. Think of ways by which you can estimate the following (where an estimate is difficult to obtain, try to get an upper bound on the quantity):

the total mass of rain-bearing clouds over India during the Monsoon

#### Solution 1

During monsoons, a metrologist records about 215 cm of rainfall in India i.e., the height of water column,* h* = 215 cm = 2.15 m

Area of country, *A* = 3.3 × 10^{12} m^{2}

Hence, volume of rain water, *V *= *A* × *h* = 7.09 × 10^{12} m^{3}

Density of water, *ρ* = 1 × 10^{3} kg m^{–3}

Hence, mass of rain water = *ρ* × *V* = 7.09 × 10^{15} kg

#### Solution 2

The average rainfall of nearly 100 cm or 1 m is recorded by meteorologists, during Monsoon, in India.

If A is the area of the country, then A = 3.3 million sq. km = 3.3 x 10^{6}(km)2 = 3.3 x 10^{6 }x 10^{6}m^{2}= 3.3 x 10^{12}m^{2}

Mass of rain-bearing clouds = area x height x density = 3.3 x 10^{12} x 1 x 1000 kg = 3.3 x 10^{15} kg.