Question

Accumulated rainfall is often measured in mm. If the density of rain water is 1000 kg/m\(^3\) then, one mm of rain is equal to ......... kg/m\(^2\) of rain. (in integer).

Hint:

1 mm of rain is equivalent to 1 kg of water over an area of 1 m\(^2\), assuming the density of water is 1000 kg/m\(^3\).

Answer 1

One mm of rainfall corresponds to a depth of 1 mm of water over a unit area (1 m\(^2\)).
Since the density of water is given as 1000 kg/m\(^3\), we can calculate the mass of 1 mm of rain over 1 m\(^2\) as follows: \[ {Mass of rain} = {density} \times {volume} = 1000 \, {kg/m}^3 \times 1 \, {mm} \times 1 \, {m}^2 = 1000 \times 10^{-3} = 1 \, {kg/m}^2 \] Thus, 1 mm of rain is equal to 1 kg/m\(^2\) of rain.