Algebra.Com's Answer #845049 by ikleyn(52803)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "water runs into a conical tank at the rate of 8 cubic meters per hour.
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document.write( "if the height of the cone is 10 meters, and the diameter of its opening is 12 meters,
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document.write( "how fast is the water level rising when the water is 3 meters deep?
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document.write( "The part of the conical tank, occupied by water, is the cone with the ratio radius to the height\r\n" );
document.write( "of  =  = 0.6.\r\n" );
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document.write( "Hence, the volume of the water in the tank at every time moment t is\r\n" );
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document.write( " V(t) =  =  =  . (1)\r\n" );
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document.write( "Differentiate it by the time\r\n" );
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document.write( "  =  . (2)\r\n" );
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document.write( " is given: it is the inflow rate, or 8 m^3/hour. \r\n" );
document.write( "Hence, when h = 3 meters deep, we have from (2)\r\n" );
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document.write( " 8 =  =  .\r\n" );
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document.write( "Hence,  =  = 0.78595 meters per hour.\r\n" );
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document.write( "Rounding to 3 decimals, you get the \r\n" );
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document.write( "ANSWER. When the water depth is 3 meters, the water rising rate is about 0.786 m/hour.\r\n" );
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document.write( "Solved.\r
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