Answer:
6 inches
Step-by-step explanation:
Formula for surface area of a cylinder:
[tex]SA=2\pi r^{2} +2\pi rh[/tex]
Plug in values and solve for the radius:
[tex]180\pi =2\pi r^{2} +2\pi r(9)\\[/tex]
Divide both sides by [tex]2\pi[/tex]
[tex]90=r^{2} +r(9)[/tex]
Subtract 90 from both sides
[tex]0=r^{2} +9r-90[/tex]
Use the quadratic equation to find the roots
[tex]x=(-b[/tex]±[tex]\sqrt{b^2-4ac})*\frac{1}{2a}[/tex] (sorry for formatting, Brainly doesn't
allow equations with ± in them)
[tex]x=\frac{-9+\sqrt{9^2-4*1*90} }{2(1)}[/tex] and [tex]x=\frac{-9-\sqrt{9^2-4*1*90} }{2(1)}[/tex]
[tex]x=\frac{(-9+\sqrt{81+360})}{2}[/tex] and [tex]x=\frac{(-9-\sqrt{81+360})}{2}[/tex]
[tex]x=\frac{(-9+\sqrt{441})}{2}[/tex] and [tex]x=\frac{(-9-\sqrt{441})}{2}[/tex]
[tex]x=\frac{(-9+21)}{2}[/tex] and [tex]x=\frac{(-9-21)}{2}[/tex]
[tex]x=\frac{12}{2}[/tex] and [tex]x=\frac{-30}{2}[/tex]
[tex]x=6[/tex] and [tex]x=-15[/tex]
We can't have a negative radius, so that leaves us with r=6 in.
