Question 1185274: Instructions: You are a young engineer. You are hired by the owner of a new resort to design a swimming pool that will hold a total of about 1500 cubic meters of water. Prepare 2 proposals to meet
the following conditions:
Pool A: A square with semicircles on each side, at least 1.5 meters deep
Pool B: a rectangle with semicircles, at least 1 m deep
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Okay, here are two swimming pool proposals for the new resort, designed to hold approximately 1500 cubic meters of water:
**Proposal 1: Pool A (Square with Semicircles)**
* **Shape:** A square with semicircles attached to each of its four sides.
* **Depth:** Minimum 1.5 meters.
* **Volume Calculation:**
* Let 's' be the side length of the square.
* The diameter of each semicircle is also 's'.
* The area of the square is s².
* The area of the four semicircles combined is equal to the area of two full circles: 2 * π * (s/2)² = (πs²)/2
* Total surface area of the pool (ignoring depth) = s² + (πs²)/2 = s²(1 + π/2)
* Volume = s²(1 + π/2) * depth
* **Design:**
* We need to find 's' such that the volume is approximately 1500 m³. Let's assume a depth of 1.5m
* 1500 ≈ s²(1 + π/2) * 1.5
* 1000 ≈ s²(1 + π/2)
* 1000 ≈ s² * 2.57
* s² ≈ 389
* s ≈ √389 ≈ 19.7 meters
* Therefore, the side of the square should be about 19.7 meters.
* The diameter of the semicircles is also about 19.7 meters.
* **Advantages:** Unique design, visually appealing.
* **Disadvantages:** Might be slightly more expensive to construct due to the curved edges.
**Proposal 2: Pool B (Rectangle with Semicircles)**
* **Shape:** A rectangle with semicircles attached to each of the shorter sides.
* **Depth:** Minimum 1 meter.
* **Volume Calculation:**
* Let 'l' be the length of the rectangle and 'w' be the width (which is also the diameter of the semicircles).
* The area of the rectangle is l * w.
* The area of the two semicircles combined is equal to the area of one full circle: π * (w/2)² = (πw²)/4
* Total surface area of the pool (ignoring depth) = l * w + (πw²)/4
* Volume = (l * w + (πw²)/4) * depth
* **Design:**
* We need to find 'l' and 'w' such that the volume is approximately 1500 m³. Let's assume a depth of 1 m.
* Let's also assume the width is half the length (w = l/2) for a reasonable looking pool.
* 1500 ≈ (l * l/2 + (π(l/2)²)/4) * 1
* 1500 ≈ (l²/2 + πl²/16)
* 1500 ≈ l²(1/2 + π/16)
* 1500 ≈ l² * 0.696
* l² ≈ 2155
* l ≈ √2155 ≈ 46.4 meters
* w = l/2 ≈ 23.2 meters
* **Advantages:** More traditional shape, potentially easier and cheaper to build than Pool A.
* **Disadvantages:** Less visually interesting than Pool A.
**Important Considerations for Both Proposals:**
* **Liner:** Both pools will need a suitable liner material.
* **Filtration System:** A robust filtration system is essential for maintaining water quality.
* **Decking:** The surrounding area will need appropriate decking.
* **Safety:** Safety features like ladders, depth markers, and lifeguard stations should be included.
* **Cost:** Detailed cost estimates should be developed for each proposal.
These proposals provide a starting point. Further refinement and engineering calculations will be necessary before construction can begin. I recommend consulting with a pool construction specialist to finalize the design and ensure it meets all safety and building codes.
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