the formula for the surface area of a cylinder with radius r and height h is [tex]2 \pi r^2 + h*2 \pi r[/tex]
since h=11, substitute into the formula to get [tex]2 \pi r^2 + 11*2 \pi r=1106[/tex]
[tex]2 \pi r^2 + 22 \pi r= 1106[/tex]
[tex]\pi r^2 + 11\pi r= 553[/tex]
since the total surface area isn't given in pi units, we can set pi=3.14
[tex]3.14r^2 + 11*3.14 r= 553[/tex]
[tex]3.14r^2 + 34.54 r= 553[/tex]
[tex]3.14r^2 + 34.54 r-553=0[/tex]
[tex]314r^2 + 3454 r-55300=0[/tex]
[tex]157r^2 + 1727 r-27650=0[/tex]
[tex]\boxed{r\approx 9 cm}[/tex]
