document.write( "Question 1186841: A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. Water is flowing into the tank at a rate of 5 cubic feet per minute. Find the rate of change of the depth of the water when the water is 6 feet deep.
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Algebra.Com's Answer #849344 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "A conical tank (with vertex down) is 10 feet across the top and 12 feet deep.
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document.write( "                 S t e p   b y   s t e p\r\n" );
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document.write( "(1)  The formula for the tank radius as the function of the depth is\r\n" );
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document.write( "         R = .     (1)\r\n" );
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document.write( "     Indeed, it gives the radius  R = 5 ft, when H = 12 ft.\r\n" );
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document.write( "(2)   The formula for the volume of the tank\r\n" );
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document.write( "          V =  =     (2)\r\n" );
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document.write( "       after substituting (1).\r\n" );
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document.write( "(3)  Differentiate it \r\n" );
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document.write( "           = .\r\n" );
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document.write( "(4)  Substitute H(t) = 6 feet and  = 3.14159265\r\n" );
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document.write( "            =  = .\r\n" );
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document.write( "(5)  Substitute   = 5 cubic feet per minute\r\n" );
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document.write( "           5 = .\r\n" );
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document.write( "(6)  From this, find\r\n" );
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document.write( "             =  = 0.254647909  feet per minute.\r\n" );
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document.write( "(7)  Round and get the ANSWER:  the rate of change of the depth of the water \r\n" );
document.write( "     is  0.25465 feet per minute when the water is 6 feet deep.\r\n" );
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