Question

Help please and thanks! I'll award brainliest if you show your work as well :)

Answer 1

Answer:

6 inches

Step-by-step explanation:

Formula for surface area of a cylinder:

$SA=2\pi r^{2} +2\pi rh$

Plug in values and solve for the radius:

$180\pi =2\pi r^{2} +2\pi r(9)$

Divide both sides by $2\pi$

$90=r^{2} +r(9)$

Subtract 90 from both sides

$0=r^{2} +9r-90$

Use the quadratic equation to find the roots

$x=(-b$±$\sqrt{b^2-4ac})*\frac{1}{2a}$ (sorry for formatting, Brainly doesn't

                                           allow equations with ± in them)

$x=\frac{-9+\sqrt{9^2-4*1*90} }{2(1)}$        and          $x=\frac{-9-\sqrt{9^2-4*1*90} }{2(1)}$

$x=\frac{(-9+\sqrt{81+360})}{2}$          and          $x=\frac{(-9-\sqrt{81+360})}{2}$

$x=\frac{(-9+\sqrt{441})}{2}$               and          $x=\frac{(-9-\sqrt{441})}{2}$

$x=\frac{(-9+21)}{2}$                   and          $x=\frac{(-9-21)}{2}$

$x=\frac{12}{2}$                           and          $x=\frac{-30}{2}$

$x=6$                             and          $x=-15$  

We can't have a negative radius, so that leaves us with r=6 in.