document.write( "Question 386510: A solid metal ball of radius 2 cm is melted and the metal obtained recast to form a solid right circular cone of radius 5 cm. Find the height of the cone. \n" ); document.write( "

Algebra.Com's Answer #273244 by Fombitz(32388) $\"\"$ $\"About$

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The volume of the metal remains the same.
\n" ); document.write( "For a sphere,
\n" ); document.write( " $\"V%5Bs%5D=%284%2F3%29pi%2AR%5E3\"$
\n" ); document.write( " $\"V%5Bs%5D=%284%2F3%29pi%2A2%5E3\"$
\n" ); document.write( " $\"V%5Bs%5D=%2832%2F3%29pi\"$
\n" ); document.write( "For a cone,
\n" ); document.write( " $\"V%5Bc%5D=%28pi%2F3%29r%5E2%2Ah\"$
\n" ); document.write( " $\"V%5Bc%5D=%28%285%2Api%29%2F3%29r%5E2\"$
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( ".
\n" ); document.write( " $\"V%5Bc%5D=V%5Bs%5D\"$
\n" ); document.write( " $\"%28%285%2Api%29%2F3%29r%5E2=%2832%2F3%29pi\"$
\n" ); document.write( " $\"5r%5E2=32\"$
\n" ); document.write( " $\"r%5E2=32%2F5\"$
\n" ); document.write( " $\"r=sqrt%2832%2F5%29\"$
\n" ); document.write( " $\"r=sqrt%28160%29%2F5\"$
\n" ); document.write( " $\"highlight%28r=%284%2F5%29sqrt%2810%29%29\"$
\n" ); document.write( " \n" ); document.write( "

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