The lateral surface area of a cylinder is 1106 cm2. Given that the height is 11 cm, calculate the radius. Answer to the nearest cm.

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

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