document.write( "Question 1106544: A close cylindrical tank 10ft in height and 4ft in diameter contains water with depth of 3ft and 5 inches. What would be the height of the water when the tank is lying in a horrizontal position? \n" ); document.write( "

Algebra.Com's Answer #721596 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "A close cylindrical tank 10ft in height and 4ft in diameter contains water with depth of 3ft and 5 inches.
\n" ); document.write( "What would be the height of the water when the tank is lying in a horrizontal position?
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document.write( "First, convert dimensions from feet to inches:  H = 10 ft = 120 in,  h = 3 feet 5 inches = 12*3+5 = 41 in,  r = 2 ft = 24 inches.\r\n" );
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document.write( "The volume of the tank is  V =  =  = .\r\n" );
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document.write( "The filled volume of the tank is  F =  = .\r\n" );
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document.write( "The ratio of the filled part to the total volume is   = .\r\n" );
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document.write( "In any position (vertical/horizontal) the filled part is   of the total volume.\r\n" );
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document.write( "Hence, we need to find the central angle of the circle which subtends the segment of the circle whose area is  of the circle area.\r\n" );
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document.write( "The area of the segment of a circle is  A = ,  where  is the central angle in radians.\r\n" );
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document.write( "Hence, we need to solve the equation\r\n" );
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document.write( " = ,\r\n" );
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document.write( "or, canceling r^2 in both sides\r\n" );
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document.write( " =  = 1.07283.\r\n" );
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document.write( "I solved this non-linear equation using Excel function  \"Goal Seek\" of  the section \"What-if\"  in my computer.\r\n" );
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document.write( "The answer is  = 2.633 radians.\r\n" );
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document.write( "Since the problem asks about the depth, it is   =  = 17.96 inches.     (24 = 24 inches = r = 2 ft is the radius)\r\n" );
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\n" ); document.write( "\n" ); document.write( "Answer. The depth under the question is 17.96 inches.\r
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