document.write( "Question 1189057: On a sphere of diameter 125cm, two circles of the sphere whose planes are parallel have a radii 23cm and 53cm, respectively. Find the area of the zone included between these circle. \n" ); document.write( "

Algebra.Com's Answer #820302 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Instead of doing it  for you, I'm going to show you how in detail:\r\n" );
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document.write( "We want the curved area on the outside of the flat-bottomed bowl\r\n" );
document.write( "on the right, not including the area of its flat circular bottom.\r\n" );
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document.write( "The area of the outside of a FLAT-bottomed bowl (not including \r\n" );
document.write( "the flat bottom), cut from a sphere, is called a 'zone'.\r\n" );
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document.write( "The area of the outside of a ROUND-bottomed bowl, cut from a \r\n" );
document.write( "sphere, is called a 'cap'.\r\n" );
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document.write( "You can do this with calculus but there is a well-known formula \r\n" );
document.write( "for the area of the cap of a sphere. That formula is\r\n" );
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document.write( "The desired area is the difference between these two caps (round \r\n" );
document.write( "bottom bowls):\r\n" );
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document.write( "Now if we only had h, we could simply plug in the formula:\r\n" );
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document.write( "Here's how we find h.  We go back and draw lines up to the \r\n" );
document.write( "center of the sphere and a radius to an edge of the bowl.  Since \r\n" );
document.write( "the diameter of the sphere is given as 125, its radius is half of \r\n" );
document.write( "that or r=62.5.\r\n" );
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document.write( "Now you can finish.  Here's how:\r\n" );
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document.write( "1. Find the red line by the Pythagorean theorem.\r\n" );
document.write( "2. Notice the red vertical line in the middle, which tells you \r\n" );
document.write( "that the vertical from the center of the sphere to the bottom \r\n" );
document.write( "of the bowl is also a radius and has length 62.5.\r\n" );
document.write( "3. Subtract what you got from step 1 from the radius 62.5. That \r\n" );
document.write( "will give you the value of h.\r\n" );
document.write( "4. Substitute in the formula: \r\n" );
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document.write( "Now you finish on your own.\r\n" );
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document.write( "Edwin

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