document.write( "Question 1093595: the diameter of a sphere and the base of a cone is equal. what percentage of that diameter must the cones height be so that both volumes are equal?9 \n" ); document.write( "

Algebra.Com's Answer #708197 by KMST(5328) $\"\"$ $\"About$

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The volume of a sphere of radius $\"r\"$ is $\"%284%2F3%29%2Api%2Ar%5E2\"$ .
\n" ); document.write( "The volume of a cone with radius $\"r\"$ and height $\"h\"$ is
\n" ); document.write( " $\"%281%2F3%29%2Api%2Ar%5E2%2Ah\"$ .
\n" ); document.write( "If sphere and cone with same radius have the same volume,
\n" ); document.write( " $\"%284%2F3%29%2Api%2Ar%5E3=%281%2F3%29%2Api%2Ar%5E2%2Ah\"$ .
\n" ); document.write( "That equation simplifies to
\n" ); document.write( " $\"4r=h\"$ } <--> $\"h=2%2Adiameter\"$ .
\n" ); document.write( "So the cone height needs to be twice the diameter.
\n" ); document.write( "That is $\"highlight%28%22200%25%22%29\"$ of the diameter. \n" ); document.write( "

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