document.write( "Question 1127169: A cone has the same radius and surface area as a sphere. Find the ratio of the perpendicular height of the cone to the radius \n" ); document.write( "
Algebra.Com's Answer #743580 by rothauserc(4718)\"\" \"About 
You can put this solution on YOUR website!
surface area of a cone = pi * r^2 + pi * r * l, where r is radius of the circular base, l is the slant height(l = square root(h^2 +r^2), where h is the perpendicular height of the cone)
\n" ); document.write( ":
\n" ); document.write( "surface area of a sphere = 4 * pi * r^2
\n" ); document.write( ":
\n" ); document.write( "set the formulas = to each other
\n" ); document.write( ":
\n" ); document.write( "4 * pi * r^2 = pi * r^2 + pi * r * l
\n" ); document.write( ":
\n" ); document.write( "3 * pi * r^2 = pi * r * l
\n" ); document.write( ":
\n" ); document.write( "3 * r = l
\n" ); document.write( ":
\n" ); document.write( "3 * r = square root(h^2 +r^2)
\n" ); document.write( ":
\n" ); document.write( "square both sides of the =
\n" ); document.write( ":
\n" ); document.write( "9 * r^2 = h^2 +r^2
\n" ); document.write( ":
\n" ); document.write( "r^2 = h^2/8
\n" ); document.write( ":
\n" ); document.write( "r = h/(2 * square root(2))
\n" ); document.write( ":
\n" ); document.write( "****************************
\n" ); document.write( "h/r = 2 * square root(2)
\n" ); document.write( "****************************
\n" ); document.write( ":
\n" ); document.write( " \n" ); document.write( "
\n" );