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}`