document.write( "Question 760227: If the height of cone is decreased by 64% then by what percent should the radius be raised to keep its volume same? \n" ); document.write( "
Algebra.Com's Answer #462493 by kmadison(20)\"\" \"About 
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Let r be the original radius, R the new radius, h the original height and H the new decreased height. Then we have: \r
\n" ); document.write( "\n" ); document.write( "1.) volume of original cone = (1/3)pi*(r^2)*h
\n" ); document.write( "2.) volume of cylinder with decreased height = (1/3)pi*(r^2)*H (100-64 gives us the remaining height) H = .36h\r
\n" ); document.write( "\n" ); document.write( "For the volume not to change we must have:
\n" ); document.write( "(1/3)pi*(r^2)*h = (1/3)pi*(r^2)*H or (1/3)pi*(r^2)*0.36*h\r
\n" ); document.write( "\n" ); document.write( "Divide both sides by (1/3)*pi
\n" ); document.write( "(r^2)*h = 0.36*(R^2)*h\r
\n" ); document.write( "\n" ); document.write( "Divide both sides by h (we assume the height is not zero)
\n" ); document.write( "r^2 = 0.36(R^2)\r
\n" ); document.write( "\n" ); document.write( "Take the square root of both sides:
\n" ); document.write( "r = 0.6R or r = -0.6R (the negative sign only tells the direction of the cone)\r
\n" ); document.write( "\n" ); document.write( "Now divide by 0.6 or 3/5 as a fraction:
\n" ); document.write( "5/3r = R = 1 2/3r\r
\n" ); document.write( "\n" ); document.write( "So the radius needs to be increased by 2/3 to maintain the volume of the cone.\r
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