Final answer:
To find the volume of water needed to fill the swimming pool, we break it down into two parts: the shallow rectangular section and the triangular prism section representing the slope to the deep end. After calculating the volumes separately, we add them together to get the total volume of water required.
Step-by-step explanation:
The question involves calculating the volume of water needed to fill a rectangular swimming pool to a certain level, accounting for a variation in depth from the shallow to the deep end. To find the amount of water, we can break the pool into two rectangular prisms and a triangular prism to make the calculations simpler.
For the first rectangular prism representing the shallow end: Volume = length × width × depth = 6 feet × 18 feet × 3 feet. The second rectangular prism does not contain water due to being 6 inches from the top, so we do not calculate it.
The triangular prism representing the decline from shallow to deep end: Cross-sectional area = 0.5 × (depth change) × (length of the decline) = 0.5 × (9 ft - 3 ft) × 16 ft, and Volume = cross-sectional area × width = Cross-sectional area × 18 feet.
Thus, we add the volumes of the two prisms to find the total volume of water required.