document.write( "Question 1086016: a sphere of radius 5 cm and a right circular cone of base radius 5 cm and height 10 cm stand on a plane. find the position of a plane that cuts the two solids in equal circular cross sections\r
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Algebra.Com's Answer #700226 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "I think your professor wants you to calculate how high above the \r\n" );
document.write( "plane that they are standing on, must another plane, parallel to \r\n" );
document.write( "the plane they are standing on, that cuts the two solids, be so \r\n" );
document.write( "that the cross sections are two equal circles.  Think of the \r\n" );
document.write( "picture below as a mid-cross section of the sphere and the cone. \r\n" );
document.write( "The green line at the bottom represents the plane they are resting \r\n" );
document.write( "on and the red line is the plane that cuts them so that diameters \r\n" );
document.write( "AB and CD are equal, making the circles equal.  We want to find h \r\n" );
document.write( "such that AB = CD.\r\n" );
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document.write( "We redraw the figure:\r\n" );
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document.write( "ΔCEQ ∽ ΔFGQ\r\n" );
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document.write( "   <--equation 1\r\n" );
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document.write( "And by applying the Pythagorean theorem to right\r\n" );
document.write( "triangle CEP,\r\n" );
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document.write( "  <--equation 2\r\n" );
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document.write( "Solve equation 1 for x,  \r\n" );
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document.write( "Substitute in equation 2:\r\n" );
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document.write( "5r = 0;  r-4 = 0\r\n" );
document.write( " r = 0;    r = 4\r\n" );
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document.write( "Only r = 4 makes sense.  And since\r\n" );
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document.write( "OS = 5\r\n" );
document.write( "OD + DS = OS = 5\r\n" );
document.write( "x + h = 5\r\n" );
document.write( "3 + h = 5\r\n" );
document.write( "    h = 2\r\n" );
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document.write( "So the plane which is 2 units above and parallel to the \r\n" );
document.write( "plane they are standing on, cuts the sphere and cone\r\n" );
document.write( "so that the cross sections will be equal circles.  I'm \r\n" );
document.write( "pretty sure that's what you want to find.\r\n" );
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document.write( "Edwin

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