Question 109600
{{{S=pi*r*sqrt(r^2+h^2)}}} Start with the given expression



{{{S/(pi*r)=sqrt(r^2+h^2)}}} Divide both sides by {{{pi*r}}}



{{{(S/(pi*r))^2=(sqrt(r^2+h^2))^2}}} Square both sides



{{{S^2/(pi^2r^2)=r^2+h^2}}} Simplify




{{{S^2/(pi^2r^2)-r^2=h^2}}} Subtract {{{r^2}}} from both sides



{{{sqrt(S^2/(pi^2r^2)-r^2)=sqrt(h^2)}}} Take the square root of both sides



{{{h=0+-sqrt(S^2/(pi^2r^2)-r^2)}}} Simplify