Question 315592
18.Solve for the indicated letter. 
Solve the formula.
S = {{{1/3}}}{{{pi*r^2h + 4pi*rh}}} for r.
:
{{{1/3}}}{{{(pi*r^2h) + (4pi*rh)}}} = S
Multiply by 3
{{{(pi*r^2h) + 3(4pi*rh)}}} = 3S
:
{{{(pi*r^2h) + (12pi*rh)}}} = 3S
Factor out pi*h
pi*h(r^2 + 12r) = 3S
:
divide both sides by {{{pi*h)}}}
r^2 + 12r = {{{(3S)/(pi*h)}}}
:
Arrange as a quadratic equation
r^2 + 12r - ({{{(3S)/(pi*h)}}}) = 0
:
Solve for r using the quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
: 
In this equation: x = r a=1; b=12; c=-{{{(3S)/(pi*h)}}}
{{{r = (-12 +- sqrt(12^2-4*1*((-3S)/(pi*h)) ))/(2*1) }}}
:
{{{r = (-12 +- sqrt(144-4((-3S)/(pi*h)) ))/2 }}}
:
{{{r = (-12 + sqrt(144+((12S)/(pi*h)) ))/2 }}}; I think only the positive solution is wanted here