document.write( "Question 1189056: A container in the shape of a sphere of radius 6cm is filled with water to depth of 10cm. (a)Find the volume of the water (b)If the water flows out through a small hole in the bottom so that the level drops 2cm , how much water escaped.
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Algebra.Com's Answer #820316 by ikleyn(52866) $\"\"$ $\"About$

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\n" ); document.write( "A container in the shape of a sphere of radius 6cm is filled with water to depth of 10cm.
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document.write( "Use the formula for the volume of a spherical cap\r\n" );
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document.write( "    V = ,\r\n" );
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document.write( "where R is the radius of the sphere and h is the height (= the depth) of the cap.\r\n" );
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document.write( "This formula works uninterruptedly in the entire diapason from h= 0 (empty container) to h= 2R (full container).\r\n" );
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document.write( "So, in case (a) you apply the formula at R= 6 cm and h= 10 cm\r\n" );
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document.write( "    V =  = 837.76 cm^3.      ANSWER\r\n" );
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document.write( "I case (b), the final volume is\r\n" );
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document.write( "    V =  = 670.21 cm^3.\r\n" );
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document.write( "The amount of water escaped is the difference  837.76 cm^3 - 670.21 cm^3 = 167.55 cm^3.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "For the formulas on the volume of a spherical cap see these Internet sources\r
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\n" ); document.write( "\n" ); document.write( "https://mathworld.wolfram.com/SphericalCap.html\r
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\n" ); document.write( "\n" ); document.write( "https://en.wikipedia.org/wiki/Spherical_cap\r
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