A rectangular swimming pool, 30m wide, 50m long and 3 m deep, contains 600 m of water. How much more water has to be added so that the water  levels 0.2 m from the top?

To solve this problem, we need to find out how much more water needs to be added to the swimming pool so that the water level is 0.2 meters from the top. 

### Step-by-Step Solution

1. **Calculate the total volume of the pool when filled to the top:**

   The volume \( V \) of a rectangular pool can be calculated using the formula:

   \[
   V = \text{length} \times \text{width} \times \text{depth}
   \]

   Given:
   - Length \( l = 50 \) meters
   - Width \( w = 30 \) meters
   - Depth \( d = 3 \) meters

   The total volume of the pool when filled to the top is:

   \[
   V = 50 \times 30 \times 3 = 4500 \, \text{m}^3
   \]

2. **Calculate the target water level:**

   The water needs to be 0.2 meters from the top. Therefore, the depth of the water required is:

   \[
   \text{Depth of water} = 3 - 0.2 = 2.8 \, \text{meters}
   \]

   Now, let's find the volume of water needed to fill the pool to a depth of 2.8 meters:

   \[
   V_{\text{water needed}} = \text{length} \times \text{width} \times \text{depth of water}
   \]

   Substituting the values:

   \[
   V_{\text{water needed}} = 50 \times 30 \times 2.8 = 4200 \, \text{m}^3
   \]

3. **Determine how much more water is needed:**

   Currently, the pool contains 600 m³ of water. The additional volume of water needed is:

   \[
   \text{Additional water needed} = V_{\text{water needed}} - \text{current volume}
   \]

   Substituting the values:

   \[
   \text{Additional water needed} = 4200 - 600 = 3600 \, \text{m}^3
   \]

### Conclusion

The pool needs **3600 cubic meters** more water to reach a level that is 0.2 meters from the top.

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Would you like more details, or do you have any questions?

Here are some related questions:
1. How do you calculate the volume of a swimming pool of different shapes?
2. How does the volume of water change with different depths?
3. What is the relationship between volume and capacity in practical applications?
4. How would the volume calculation change if the pool were not rectangular?
5. What are other methods to measure large quantities of water in practice?

**Tip:** Always double-check your unit conversions when solving real-world math problems!

Explore how to calculate the volume of water needed in a rectangular swimming pool, given its dimensions and current water level. Learn step-by-step with a detailed solution covering geometry and volume calculations.

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