Question

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

Hint:

A quick memory trick: 1 mm of rainfall depth corresponds to \(1~\mathrm{L/m^2}\) or \(1~\mathrm{kg/m^2}\).

Answer 1

Correct Answer: 1

Step 1: Convert 1 mm rainfall into depth.
1 mm = \(0.001~\mathrm{m}\). This means a water column of height \(0.001~\mathrm{m}\) over 1 square metre of area.


Step 2: Volume of water per unit area.
Volume = depth \(\times\) area = \(0.001 \times 1 = 0.001~\mathrm{m^3/m^2}\).


Step 3: Mass of water.
Mass = density \(\times\) volume = \(1000 \times 0.001 = 1~\mathrm{kg/m^2}\).
Final Answer:
\[ \boxed{1~\mathrm{kg/m^2}} \]