To determine the height of the swimming pool, we need to use the relationship between the volume of the pool and its dimensions. Here's a step-by-step solution:
1. Understanding the given data:
- The capacity of the swimming pool is 3000 kiloliters (kl).
- The length of the swimming pool is 50 meters (m).
- The width of the swimming pool is 20 meters (m).
2. Unit Conversion:
- 1 kiloliter (kl) is equivalent to 1 cubic meter (m³). Therefore, 3000 kiloliters is equal to 3000 cubic meters (m³).
3. Volume Formula:
- The volume [tex]\(V\)[/tex] of a rectangular prism (which the swimming pool resembles) is given by the formula:
[tex]\[
V = \text{length} \times \text{width} \times \text{height}
\][/tex]
In our case:
[tex]\[
V = 3000 \, \text{m}^3
\][/tex]
[tex]\[
\text{length} = 50 \, \text{m}
\][/tex]
[tex]\[
\text{width} = 20 \, \text{m}
\][/tex]
We need to find the height [tex]\(h\)[/tex].
4. Rearranging the formula to solve for height:
[tex]\[
h = \frac{V}{\text{length} \times \text{width}}
\][/tex]
5. Substituting the given values:
[tex]\[
h = \frac{3000 \, \text{m}^3}{50 \, \text{m} \times 20 \, \text{m}}
\][/tex]
6. Performing the calculation:
[tex]\[
h = \frac{3000 \, \text{m}^3}{1000 \, \text{m}^2}
\][/tex]
Simplifying the right-hand side:
[tex]\[
h = 3 \, \text{m}
\][/tex]
So, the height of the swimming pool is 3 meters.
