Question:easy

1 cm of rainfall over a catchment area of 1 \(\text{km}^2\) represents a volume of water equal to:

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Keep these direct conversion shortcuts handy for hydrological exams:
- \(1\text{ mm of rain over 1 ha} = 10\text{ m}^3\).
- \(1\text{ cm of rain over 1 ha} = 100\text{ m}^3\).
- \(1\text{ cm of rain over 1 km}^2 = 10,000\text{ m}^3 = 10^4\text{ m}^3\).
  • \(10^4 \text{ m}^3\)
  • \(10^4 \text{ m}^2\)
  • \(10^4 \text{ m}^4\)
  • \(10^3 \text{ m}^3\)
Show Solution

The Correct Option is A

Solution and Explanation

Step 1: Convert both given quantities into a single consistent unit system.
Convert 1 cm of rainfall depth to metres, \( 1 \text{ cm} = 0.01 \text{ m} \). Convert the catchment area from square kilometres to square metres, \( 1 \text{ km}^2 = (1000 \text{ m})^2 = 10^6 \text{ m}^2 \).
Step 2: Apply the basic definition of rainfall volume.
Volume of rainfall over a catchment equals the depth of rain multiplied by the catchment area, treating the catchment as flat for this purpose: \[ V = d \times A \]
Step 3: Substitute the converted values and simplify.
\[ V = 0.01 \text{ m} \times 10^6 \text{ m}^2 = 10^4 \text{ m}^3 \] The units work out correctly, metres times square metres gives cubic metres, a true volume, which also rules out the options that leave the answer in square metres or metres to the fourth power.
\[ \boxed{10^4 \text{ m}^3} \]
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