s=2pirh+pir^2 solve for r

Question

S=pirh+pir^2 solve for r is an Algebra 2 problem and I have been trying to solve it for hours. Help!!

Answer 1

This seems to be the formula for the total surface area of a cylinder. If so, it should be: s = 2πrh + 2πr². However, let's go with what you have: s = 2πrh + πr²   or s = 2πhr + πr²   

 

If you treat this as a quadratic equation (and for now assume h and s are constants), then we can rearrange the equation to be:

 

 πr²  +  2πhr  - s = 0

 

If you know the quadratic formula, then r = -2πh ± √[(2πh)² - 4π(-s)] /2π

                                                                           

 

If you simplify this, you get:    r = -πh ± √[π²h² + πs]/π