Sure, let's break down the problem step-by-step to find the height (or depth) of the water in the pool.
### Problem:
Given:
- Length of the pool (L) = 29 feet
- Width of the pool (W) = 14 feet
- Volume of water in the pool (V) = 1,827 cubic feet
We need to find the height (H) of the water in the pool.
### Step-by-Step Solution:
1. Consider the formula for the volume of a rectangular prism:
[tex]\[ V = L \times W \times H \][/tex]
2. We need to solve for the height [tex]\( H \)[/tex]:
[tex]\[ H = \frac{V}{L \times W} \][/tex]
3. Substitute the given values into the formula:
[tex]\[ H = \frac{1827 \, \text{cubic feet}}{29 \, \text{feet} \times 14 \, \text{feet}} \][/tex]
4. Perform the multiplication in the denominator first:
[tex]\[ 29 \times 14 = 406 \][/tex]
5. Now, divide the volume by the area of the base:
[tex]\[ H = \frac{1827}{406} \][/tex]
6. Perform the division to find the height:
[tex]\[ H = 4.5 \, \text{feet} \][/tex]
So, the height of the water above the base of the pool is 4.5 feet.
### Diagram:
Below is a simple diagram of the swimming pool:
```
Length = 29 feet
+-----------------------+
| |
Width | |
= | |
14 | | Height = 4.5 feet
feet | |
| |
+-----------------------+
```
This diagram shows a side view of the swimming pool where the length and width form the base, and the height represents the depth of the water.
