How do I solve for r?

Question

S=2πrh+2πr²

Answer 1

2πrh + 2πr² = S

 

(2π)r² + (2πh)r - S = 0  ← Equation has the form Ar² + Br + C = 0, with                                      A = 2π, B = 2πh, C = -S

 

Using the quadratic formula, r = [-2πh ± √((2πh)² - 4(2π)(-S))]/(4π)

 

                                          = [-2πh ± √(4πh²+8πS)]/(4π)

 

                                          = [-2πh ± 2√(πh² + 2πS)]/(4π)

 

                                          = [-πh ± √(πh² + 2πS)]/(2π)