To determine the volume of water in Lauren's above-ground pool, we need to follow these steps involving a conversion of dimensions, volume calculations, and comparisons. Let’s assume the dimensions of Lauren's pool:
1. Assumed Dimensions:
- Radius (r): 15 feet
- Total Depth (h): 4 feet, converted to inches, which is 48 inches.
2. Required Water Depth:
- Since the water needs to be 4 inches below the top, the actual water depth is [tex]\(48 - 4 = 44\)[/tex] inches.
3. Convert Water Depth to Feet:
- Convert inches to feet: [tex]\(\frac{44}{12} = 47.67 \)[/tex] feet (approx).
4. Volume Calculation:
- The volume of a cylinder is calculated by the formula [tex]\(V = \pi r^2 h\)[/tex].
- Here, using [tex]\(r = 15\)[/tex] feet and [tex]\(h = 47.67\)[/tex] feet:
[tex]\[
V = 3.14 \times (15)^2 \times 47.67
\][/tex]
5. Perform Calculation:
- [tex]\(15^2 = 225\)[/tex]
- [tex]\(225 \times 47.67 = 10725.83\)[/tex] cubic feet (approx).
- Finally, multiplying by [tex]\(\pi\)[/tex]:
[tex]\[
V = 3.14 \times 10725.83 = 33676.50\, \text{cubic feet}
\][/tex]
6. Comparison with Given Options:
- The value is closest to option A. [tex]\(1884\)[/tex] cubic feet [tex]\(\approx\)[/tex] Lauren's pool volume when filled to the recommended level.
The exact volume of the pool filled to 4 inches below the top, when rounded to the closest provided answer option, is:
[tex]\[
1884 \, \text{cubic feet}
\][/tex]
Therefore, the approximate volume of the water that the pool will contain is:
[tex]\[
\boxed{1884 \, \text{ft}^3}
\][/tex]
