document.write( "Question 1085826: a wooden pyramid is to be cut into 2 parts of equal weights by a plane parallel to its base. find the ratio of the heights of the two parts \n" ); document.write( "

Algebra.Com's Answer #700195 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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A wooden pyramid is to be cut into 2 parts of equal weights by a plane parallel to its base.
\n" ); document.write( " Find the ratio of the heights of the two parts.
\n" ); document.write( ":
\n" ); document.write( "Use an example the original pyramid: base = 100 sq/units, height = 12 unit
\n" ); document.write( " $\"1%2F3\"$ *100*12 = 400 cu/units
\n" ); document.write( "By what percent x,(decimal form) do we have to reduce the base area and height to get a vol of 200 cu/units
\n" ); document.write( " $\"1%2F3\"$ *100x * 12x = 200
\n" ); document.write( " $\"%281200x%5E2%29%2F3\"$ = 200
\n" ); document.write( "400x^2 = 200
\n" ); document.write( "x^2 = $\"200%2F400\"$
\n" ); document.write( "x^2 = .5
\n" ); document.write( "x = $\"sqrt%28.5%29\"$
\n" ); document.write( "x = .707
\n" ); document.write( " check the half pyramid vol
\n" ); document.write( " $\"1%2F3\"$ .707(100) * .707(12) =
\n" ); document.write( " $\"%2870.7+%2A+8.485%29%2F3\"$ = 199.97 ~ 200
\n" ); document.write( ":
\n" ); document.write( "Ratio of the heights 1:707
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