document.write( "Question 1088524: find what fraction of the altitude of a tetrahedron must be cut off by a plane parallel to the base of the tetrahedron such that the volume of the cut off tetrahedron is one third of the original volume. \n" ); document.write( "

Algebra.Com's Answer #702799 by KMST(5328) $\"\"$ $\"About$

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Compared to the original tetrahedron, the smaller tetrahedron cut off is a similar shape, meaning a scaled-down version.
\n" ); document.write( "For similar shapes, the ratios of lengths (L and l), surface areas (A and a), and volumes (V and v) are related by
\n" ); document.write( " $\"v%2FV=%28l%2FL%29%5E3\"$ and $\"a%2FA=%28l%2FL%29%5E2\"$ .
\n" ); document.write( "In this case, if $\"x\"$ is the fraction of the altitude of a tetrahedron cut off by a plane parallel to the base of the tetrahedron,
\n" ); document.write( "and the volume of the small cut off tetrahedron is one third of the original volume,
\n" ); document.write( " $\"1%2F3=x%5E3\"$ --> $\"x=root%283%2C1%2F3%29=root%283%2C9%2F27%29=root%283%2C9%29%2F3=about0.693\"$ .
\n" ); document.write( "The exact result is an irrational number, so it cannot be expressed as a fraction.
\n" ); document.write( "However, the fractions $\"52%2F75\"$ and $\"658%2F949\"$ are good approximate values. \n" ); document.write( "

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