Question

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.

Answer 1

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
$3.14r^2 + 11*3.14 r= 553$
$3.14r^2 + 34.54 r= 553$
$3.14r^2 + 34.54 r-553=0$
$314r^2 + 3454 r-55300=0$
$157r^2 + 1727 r-27650=0$
$\boxed{r\approx 9 cm}$