document.write( "Question 1173952: A spheroid (or oblate spheroid) is a surface obtained by rotating an ellipse around its minor axis the ball in figure 1.41 is in the shape of the lower half of a spheroid that is its horizontal cross-section as circles well its vertical cross-section that pass through the center a semi-ellipse s if this bowl is 10 inch wide at the opening and square root 10 in deep at the center how deep does a circular cover with diameter 9 in go into the bowl \n" ); document.write( "

Algebra.Com's Answer #850734 by ikleyn(52817) $\"\"$ $\"About$

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\n" ); document.write( "A spheroid (or oblate spheroid) is a surface obtained by rotating an ellipse around its minor axis
\n" ); document.write( "the ball in figure 1.41 is in the shape of the lower half of a spheroid that is its horizontal
\n" ); document.write( "cross-section as circles well its vertical cross-section that pass through the center a semi-ellipse
\n" ); document.write( "s if this bowl is 10 inch wide at the opening and square root 10 in deep at the center
\n" ); document.write( "how deep does a circular cover with diameter 9 in go into the bowl
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\n" ); document.write( "\n" ); document.write( "        The solution to the problem in the post by @CPhill, giving the answer of 0.02 inches \r
\n" ); document.write( "\n" ); document.write( "        for the depth of the cover is INCORRECT conceptually, since it uses wrong ideas.\r
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\n" ); document.write( "\n" ); document.write( "        I came to bring a correct solution.\r
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document.write( "To solve the problem, it is enough to consider vertical section through the vertical axis of rotation.\r\n" );
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document.write( "In vertical section, we have the lover half of the ellipse with the horizontal major semi-axis \r\n" );
document.write( "of a = 10/2 = 5 inches long and vertical minor semi-axis of b =  inches long.\r\n" );
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document.write( "The equation of the ellipse is\r\n" );
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document.write( "     +  = 1,    (1)\r\n" );
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document.write( "or\r\n" );
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document.write( "     +  = 1.    (2)\r\n" );
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document.write( "We are given x = 4.5 inches for the edge of the cover, and we want to find y.\r\n" );
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document.write( "From equation (2)\r\n" );
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document.write( "    y = +/-  = +/-  = 1.378405 inches.\r\n" );
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document.write( "We round it reasonably and get for the depth of the cover\r\n" );
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document.write( "ANSWER.  1.4 inches, approximately.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved correctly.\r
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