Question

Water resources are often reported in Billion \(\text{M}^3\), \(\text{Km}^3\) and Million ha-m (m ha-m). Which two of these are the same?

• A. Billion \(\text{M}^3\) and M ha-m
• B. Billion \(\text{M}^3\) and \(\text{Km}^3\)
• C. \(\text{Km}^3\) and Million ha-m
• D. None of the three are equal

Hint:

Conversion rule: $1\text{ Km}^3 = 1\text{ Billion m}^3 = 1\text{ BCM} = 0.1\text{ M ha-m}$ ($1\text{ M ha-m} = 10\text{ BCM} = 10\text{ Km}^3$).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Volumetric water resources reporting in hydrology uses cubic kilometers, billion cubic meters (BCM), and million hectare-meters (M ha-m).
Key Formula or Approach:
\[ 1\text{ km} = 1000\text{ m} \implies 1\text{ km}^3 = (10^3\text{ m})^3 = 10^9\text{ m}^3 = 1\text{ Billion m}^3 \]
\[ 1\text{ ha-m} = 10^4\text{ m}^2 \times 1\text{ m} = 10^4\text{ m}^3 \implies 1\text{ M ha-m} = 10^6 \times 10^4 = 10^{10}\text{ m}^3 = 10\text{ km}^3 \]

Step 2: Detailed Explanation:
Converting each volumetric unit to cubic meters ($\text{m}^3$):
1. 1 \(\text{Km}^3\):
\[ 1\text{ km}^3 = 1000\text{ m} \times 1000\text{ m} \times 1000\text{ m} = 10^9\text{ m}^3 = 1\text{ Billion m}^3 \]
2. 1 Billion \(\text{M}^3\) (BCM):
\[ 1\text{ Billion m}^3 = 10^9\text{ m}^3 \]
3. 1 Million ha-m (M ha-m):
\[ 1\text{ M ha-m} = 10^6 \times 10^4\text{ m}^3 = 10^{10}\text{ m}^3 = 10\text{ km}^3 = 10\text{ Billion m}^3 \]
Therefore, \(\text{Billion M}^3\) and \(\text{Km}^3\) are exactly identical.

Step 3: Final Answer:
Hence, Billion \(\text{M}^3\) and \(\text{Km}^3\) are the same, matching option (B).