2 cm of rain has fallen on a square kilometer of land. Assuming that 50% of the rain drops could have been collected and contained in a pool having a `100 m xx 10 m` base, by what level would the water level in the pool have increased?

Options

A. 15 m
B. 20 m
C. 10 m
D. 25 m

Answer

To solve the problem, we need to follow these steps:

### Step 1: Calculate the volume of rain that fell on the land.
- The area of the land is given as 1 square kilometer, which is equal to \( 1,000,000 \, \text{m}^2 \).
- The height of the rain is given as 2 cm, which is equal to \( 0.02 \, \text{m} \).
- The volume of rain that fell can be calculated using the formula:
\[ \text{Volume} = \text{Area} \times \text{Height} \]
\[ \text{Volume} = 1,000,000 \, \text{m}^2 \times 0.02 \, \text{m} = 20,000 \, \text{m}^3 \]

### Step 2: Calculate the volume of rain that can be collected.
- Since only 50% of the rain can be collected, we calculate:
\[ \text{Collected Volume} = 0.5 \times 20,000 \, \text{m}^3 = 10,000 \, \text{m}^3 \]

### Step 3: Calculate the dimensions of the pool.
- The base area of the pool is given as \( 100 \, \text{m} \times 10 \, \text{m} \).
- Therefore, the base area of the pool is:
\[ \text{Base Area} = 100 \, \text{m} \times 10 \, \text{m} = 1,000 \, \text{m}^2 \]

### Step 4: Calculate the increase in water level in the pool.
- To find the increase in water level, we use the formula:
\[ \text{Increase in Height} = \frac{\text{Collected Volume}}{\text{Base Area}} \]
\[ \text{Increase in Height} = \frac{10,000 \, \text{m}^3}{1,000 \, \text{m}^2} = 10 \, \text{m} \]

### Final Answer:
The water level in the pool would have increased by **10 meters**.

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