document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201828>Question 1201828</A>: <I><SPAN STYLE=\"word-break: break-all;\"> water is flowing through a pipe with radius 14 cm.The maximum depth of the water is 9 cm.What is the width,PQ,of the surface of the water? </SPAN>\n" );
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document.write( "Answer: <BR>\n" );
document.write( "<font color=red>6*sqrt(5) centimeters</font> exactly<BR>\n" );
document.write( "6*sqrt(5) = <font color=red>13.4164078649987 centimeters</font> approximately<BR>\n" );
document.write( "Round that approximate value however needed.\r<BR>\n" );
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document.write( "Work Shown:\r<BR>\n" );
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document.write( "This is what the diagram probably looks like<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0Adrawing%28300%2C300%2C-5%2C5%2C-5%2C5%2C%0D%0Acircle%280%2C0%2C3%29%2C%0D%0Aline%280%2C0%2C0%2C-3%29%2C%0D%0Ablue%28%0D%0Aline%28-2.4%2C-sqrt%289-%282.4%29%5E2%29%2C2.4%2C-sqrt%289-%282.4%29%5E2%29%29%2Cline%28-2.38%2C-sqrt%289-%282.38%29%5E2%29%2C2.38%2C-sqrt%289-%282.38%29%5E2%29%29%2Cline%28-2.36%2C-sqrt%289-%282.36%29%5E2%29%2C2.36%2C-sqrt%289-%282.36%29%5E2%29%29%2Cline%28-2.34%2C-sqrt%289-%282.34%29%5E2%29%2C2.34%2C-sqrt%289-%282.34%29%5E2%29%29%2C%0D%0Alocate%281.5%2C-1.1%2C%22x%22%29%2C%0D%0Alocate%28-1.5%2C-1.1%2C%22x%22%29%0D%0A%29%2C%0D%0Alocate%280.1%2C-0.5%2C%225%22%29%2C%0D%0Alocate%280.1%2C-2%2C%229%22%29%2C%0D%0Alocate%28-4%2C-4%2Cmatrix%281%2C4%2CDiagram%2Cnot%2Cto%2Cscale%29%29%0D%0A%29%0D%0A ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The diagram is not to scale.<BR>\n" );
document.write( "The radius 14 cm is broken down into the pieces 5 cm and 9 cm.<BR>\n" );
document.write( "The water's height is 9 cm, and the remaining 5 cm is the gap from the water line to the center of the circle.<BR>\n" );
document.write( "The radius bisects the chord, meaning each smaller congruent piece is x cm long.\r<BR>\n" );
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document.write( "Apply the intersecting chords theorem<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.mathsisfun.com/geometry/circle-intersect-chords.html\">https://www.mathsisfun.com/geometry/circle-intersect-chords.html</a><BR>\n" );
document.write( "and we get the following<BR>\n" );
document.write( "a*b = c*d<BR>\n" );
document.write( "x*x = 9*5<BR>\n" );
document.write( "x^2 = 9*5<BR>\n" );
document.write( "x = sqrt(9*5)<BR>\n" );
document.write( "x = sqrt(9)*sqrt(5)<BR>\n" );
document.write( "x = 3*sqrt(5)<BR>\n" );
document.write( "Therefore,<BR>\n" );
document.write( "2x = 2*3*sqrt(5) = <font color=red>6*sqrt(5)</font> represents the exact width of the water's surface when the max depth of the water is 9 cm.\r<BR>\n" );
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document.write( "6*sqrt(5) = <font color=red>13.4164078649987 approximately</font>.\r<BR>\n" );
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document.write( "Edit: I just realized I made a silly error. Refer to the solution by @ikleyn for the correct values to use in the intersecting chords theorem.<BR>\n" );
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