Given:
Given that the radius of the cylinder is 6 m.
The height of the cylinder is 7 m.
We need to determine the surface area of the cylinder.
Surface area of the cylinder:
The surface area of the cylinder can be determined using the formula,
![SA=2 \pi r(r+h)](https://img.qammunity.org/2021/formulas/mathematics/high-school/ssesrdl7h6ocuawu2z0wxraxepak17djf4.png)
where r is the radius and h is the height of the cylinder.
Substituting r = 6 and h = 7 in the above formula, we get;
![SA=2 (3.14)(6)(6+7)](https://img.qammunity.org/2021/formulas/mathematics/high-school/xf8w8jl5drhbho6j9g9jkh2lcp70q0wfan.png)
Simplifying, we get;
![SA=2 (3.14)(6)(13)](https://img.qammunity.org/2021/formulas/mathematics/high-school/4jk190k7g7yqly2hdwki0nq22mj40c1302.png)
Multiplying, we get;
![SA=489.84 \ m^2](https://img.qammunity.org/2021/formulas/mathematics/high-school/gwpizwgzsq8y8gwxd21ksn9oin37o5hv98.png)
Thus, the surface area of the cylinder is 489.84 square meters.
Hence, Option a is the correct answer.