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