document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1185274>Question 1185274</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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<BR>\n" );
document.write( "the following conditions:\r<BR>\n" );
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document.write( "Pool A: A square with semicircles on each side, at least 1.5 meters deep<BR>\n" );
document.write( "Pool B: a rectangle with semicircles, at least 1 m deep </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849764 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849764\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Okay, here are two swimming pool proposals for the new resort, designed to hold approximately 1500 cubic meters of water:\r<BR>\n" );
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document.write( "**Proposal 1: Pool A (Square with Semicircles)**\r<BR>\n" );
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document.write( "*   **Shape:** A square with semicircles attached to each of its four sides.<BR>\n" );
document.write( "*   **Depth:** Minimum 1.5 meters.<BR>\n" );
document.write( "*   **Volume Calculation:**<BR>\n" );
document.write( "    *   Let 's' be the side length of the square.<BR>\n" );
document.write( "    *   The diameter of each semicircle is also 's'.<BR>\n" );
document.write( "    *   The area of the square is s².<BR>\n" );
document.write( "    *   The area of the four semicircles combined is equal to the area of two full circles: 2 * π * (s/2)² = (πs²)/2<BR>\n" );
document.write( "    *   Total surface area of the pool (ignoring depth) = s² + (πs²)/2 = s²(1 + π/2)<BR>\n" );
document.write( "    *   Volume =  s²(1 + π/2) * depth\r<BR>\n" );
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document.write( "*   **Design:**<BR>\n" );
document.write( "    *   We need to find 's' such that the volume is approximately 1500 m³. Let's assume a depth of 1.5m<BR>\n" );
document.write( "        *   1500 ≈ s²(1 + π/2) * 1.5<BR>\n" );
document.write( "        *   1000 ≈ s²(1 + π/2)<BR>\n" );
document.write( "        *   1000 ≈ s² * 2.57<BR>\n" );
document.write( "        *   s² ≈ 389<BR>\n" );
document.write( "        *   s ≈ √389 ≈ 19.7 meters<BR>\n" );
document.write( "    *   Therefore, the side of the square should be about 19.7 meters.<BR>\n" );
document.write( "    *   The diameter of the semicircles is also about 19.7 meters.\r<BR>\n" );
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document.write( "*   **Advantages:** Unique design, visually appealing.<BR>\n" );
document.write( "*   **Disadvantages:**  Might be slightly more expensive to construct due to the curved edges.\r<BR>\n" );
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document.write( "**Proposal 2: Pool B (Rectangle with Semicircles)**\r<BR>\n" );
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document.write( "*   **Shape:** A rectangle with semicircles attached to each of the shorter sides.<BR>\n" );
document.write( "*   **Depth:** Minimum 1 meter.<BR>\n" );
document.write( "*   **Volume Calculation:**<BR>\n" );
document.write( "    *   Let 'l' be the length of the rectangle and 'w' be the width (which is also the diameter of the semicircles).<BR>\n" );
document.write( "    *   The area of the rectangle is l * w.<BR>\n" );
document.write( "    *   The area of the two semicircles combined is equal to the area of one full circle: π * (w/2)² = (πw²)/4<BR>\n" );
document.write( "    *   Total surface area of the pool (ignoring depth) = l * w + (πw²)/4<BR>\n" );
document.write( "    *   Volume = (l * w + (πw²)/4) * depth\r<BR>\n" );
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document.write( "*   **Design:**<BR>\n" );
document.write( "    *   We need to find 'l' and 'w' such that the volume is approximately 1500 m³. Let's assume a depth of 1 m.<BR>\n" );
document.write( "    *   Let's also assume the width is half the length (w = l/2) for a reasonable looking pool.<BR>\n" );
document.write( "    *   1500 ≈ (l * l/2 + (π(l/2)²)/4) * 1<BR>\n" );
document.write( "    *   1500 ≈ (l²/2 + πl²/16)<BR>\n" );
document.write( "    *   1500 ≈ l²(1/2 + π/16)<BR>\n" );
document.write( "    *   1500 ≈ l² * 0.696<BR>\n" );
document.write( "    *   l² ≈ 2155<BR>\n" );
document.write( "    *   l ≈ √2155 ≈ 46.4 meters<BR>\n" );
document.write( "    *   w = l/2 ≈ 23.2 meters\r<BR>\n" );
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document.write( "*   **Advantages:**  More traditional shape, potentially easier and cheaper to build than Pool A.<BR>\n" );
document.write( "*   **Disadvantages:** Less visually interesting than Pool A.\r<BR>\n" );
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document.write( "**Important Considerations for Both Proposals:**\r<BR>\n" );
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document.write( "*   **Liner:**  Both pools will need a suitable liner material.<BR>\n" );
document.write( "*   **Filtration System:**  A robust filtration system is essential for maintaining water quality.<BR>\n" );
document.write( "*   **Decking:**  The surrounding area will need appropriate decking.<BR>\n" );
document.write( "*   **Safety:**  Safety features like ladders, depth markers, and lifeguard stations should be included.<BR>\n" );
document.write( "*   **Cost:**  Detailed cost estimates should be developed for each proposal.\r<BR>\n" );
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document.write( "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.<BR>\n" );
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