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 #853638 by ikleyn(53618) $\"\"$ $\"About$

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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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\n" ); document.write( "\n" ); document.write( "        What is written in the post by @mananth, is FATALLY and TOTALLY wrong.\r
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\n" ); document.write( "\n" ); document.write( "        First, he MISSED the radius and diameter values in his calculations, using MISTAKENLY \r
\n" ); document.write( "\n" ); document.write( "        value of 36 inches (or 3 ft) as the radius R, while the true value of the radius is 1.5 ft.\r
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\n" ); document.write( "\n" ); document.write( "        Second, the basic calculation formula in his post is written INCORRECTLY.\r
\n" ); document.write( "\n" ); document.write( "        A reader can see that even the dimension of the second term in the formula \r
\n" ); document.write( "\n" ); document.write( "        is not the dimension of area.\r
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\n" ); document.write( "\n" ); document.write( "        Third, he suddenly uses gallons in the mid of his calculations, although it is totally different\r
\n" ); document.write( "\n" ); document.write( "        unit from cubic feet or cubic inches that are used in the input.\r
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\n" ); document.write( "\n" ); document.write( "        Fourth, the final answer absents in the post by @mananth.\r
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\n" ); document.write( "\n" ); document.write( "        From these my notes, it is clear that the solution by @mananth should be re-done from scratch.\r
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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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\n" ); document.write( "\n" ); document.write( "At this point, the problem is solved completely.\r
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\n" ); document.write( "\n" ); document.write( "After completing my solution, I found a solution to this problem by tutor @math_helper at this forum,
\n" ); document.write( "which provides the SAME answer\r
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\n" ); document.write( "\n" ); document.write( "https://www.algebra.com/algebra/homework/Bodies-in-space/Bodies-in-space.faq.question.1198022.html\r
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