263.76 cm is the minimum amount of paper she will need to wrap the entire container.
Explanation:
As we know that the equation for surface area of a cylinder,
Surface area of cylinder =
![2\pi r^(2)+2 \pi r h](https://img.qammunity.org/2021/formulas/mathematics/middle-school/c33ar995k8xe2d6c45ph20nr5cmdvhvdda.png)
Where,
r - the radius of the cylinder. Here given diameter (D) as 6. So,
![r=(D)/(2)=(6)/(2)=3 \mathrm{cm}](https://img.qammunity.org/2021/formulas/mathematics/middle-school/l121yzgmv3kwfn0lplpxt0ge9z5p5k2wdk.png)
h - the height of the cylinder (given as 11 cm). The value for pi = 3.14. Now, calculate the surface area of the cylinder as
![A=2(3.14)(3)^(2)+2(3.14)(3)(11)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/u2nfulp1loldi6ijp7shrsr5ogqnnld384.png)
A = 56.52+ 207.24 = 263.76 cm