Chapter 1 - Equations and Inequalities - 1.5 Applications and Modeling with Quadratic Equations - 1.5 Exercises - Page 131: 33

$3.75cm$

Step 1. Assume the radius is $r$, the surface area would be $A=2\pi r^2 + 2\pi rh$ where $h=12cm$ is the height. Step 2. Let $A=371cm^2$, we have $2\pi r^2 + 24\pi r=371$ or $2\pi r^2 + 24\pi r-371=0$ Step 3. Let $a=2\pi, b=24\pi, c=-371$, use the quadratic formula to solve the above equation and discard the negative answer to get $r\approx3.75cm$