document.write( "Question 1178403: a closed cylindrical tank is 8 feet long and 3 feet in diameter. when lying in a horizontal position, the water is 2 feet deep. if the tank is the vertical position, the depth of water in the tank is? \n" ); document.write( "

Algebra.Com's Answer #853640 by n2(54) $\"\"$ $\"About$

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\n" ); document.write( "a closed cylindrical tank is 8 feet long and 3 feet in diameter.
\n" ); document.write( "when lying in a horizontal position, the water is 2 feet deep.
\n" ); document.write( "if the tank is the vertical position, the depth of water in the tank is?
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document.write( "The formula for the volume of water in horizontal cylindrical tank is \r\n" );
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document.write( "    V = ,    (1)\r\n" );
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document.write( "where 'r' is the radius of the cylindrical tank and 'h' is the depth of water; L is the length of the cylinder.\r\n" );
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document.write( "This formula represents the product of the length of the container by the area of the cross-section\r\n" );
document.write( "of the tank, occupied by water.\r\n" );
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document.write( "Notice that in this problem the depth 'h' of 2 feet is greater than the radius of the tank, which is 1.5 ft.\r\n" );
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document.write( "So, the horizontal axis of the container is BELOW the water level.\r\n" );
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document.write( "Nevertheless, the formula works in this case too, without change.\r\n" );
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document.write( "Indeed, when h > r, the first term represents the area of the major sector of the circle, \r\n" );
document.write( "while the second term represents the area of the triangle, which complement the sector to the major segment.\r\n" );
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document.write( "So, we are ready to calculate. Insert the numbers instead of symbols\r\n" );
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document.write( "    V = .    (2)\r\n" );
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document.write( "We have   =  = 1.910633 radians,\r\n" );
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document.write( "          =  = -0.707107.\r\n" );
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document.write( "so we can continue formula (2) this way\r\n" );
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document.write( "    V =  = 40.04825 ft^3.\r\n" );
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document.write( "Now, to get the height of the water in vertical cylinder, we should divide this volume\r\n" );
document.write( "by the area of the base   =  = 7.0685775.\r\n" );
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document.write( "Thus we find\r\n" );
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document.write( "    the height of the water in vertical container =  = 5.665673185\r\n" );
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document.write( "or about 5.666 ft.\r\n" );
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document.write( "ANSWER.  The height of the water in vertical container is about 5.666 ft.\r\n" );
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