document.write( "Question 1082189: How far from the center of the sphere of a radius 10 cm should a plane be passed so that the ratio of surface areas of the two zones is 3:7. \n" ); document.write( "

Algebra.Com's Answer #696281 by Fombitz(32388) $\"\"$ $\"About$

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Use the area of a spherical cap,
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\n" ); document.write( " $\"SA=2pi%2AR%2Ah\"$
\n" ); document.write( "The total surface area of the sphere would occur when $\"h=2R\"$ when,
\n" ); document.write( " $\"SA%5Btot%5D=4pi%2AR%5E2\"$
\n" ); document.write( "We only want $\"3%2F%283%2B7%29=3%2F10\"$ of the total area so,
\n" ); document.write( " $\"2pi%2AR%2Ah=%283%2F10%294pi%2AR%5E2\"$
\n" ); document.write( " $\"2h=%283%2F10%294R\"$
\n" ); document.write( " $\"h=%283%2F5%29R\"$
\n" ); document.write( " $\"h=%283%2F5%29%2810%29\"$
\n" ); document.write( " $\"h=6\"$ $\"cm\"$
\n" ); document.write( "So the value we're looking for is actually the distance from the center which would be $\"R-h\"$
\n" ); document.write( " $\"R-h=10-6\"$
\n" ); document.write( " $\"R-h=4\"$ $\"cm\"$ \r
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