Explanation:
The radius of a cylinder, r = 13 feet
Height of the cylinder, h = 28 feet
The circumference of the cylinder is given by :
![C=2\pi r\\\\=2\pi * 13\\\\=81.68\ ft\\\\C=82\ ft](https://img.qammunity.org/2022/formulas/mathematics/high-school/62x3xg3xco0vrgticge77o1e1znzbekn2p.png)
The area of one base is given by :
![A=\pi r^2\\\\=\pi * 13^2\\\\=530.92\ ft^2\\\\=531\ ft^2](https://img.qammunity.org/2022/formulas/mathematics/high-school/mazyyl98uc0huf7s3wdwibuky5neht4mlg.png)
The lateral area of the cylinder is given by :
![A=2\pi r h\\\\A=2\pi* 13* 28\\\\A=2287.07\ ft^2](https://img.qammunity.org/2022/formulas/mathematics/high-school/a12jjl06jn65bmyomfxmtlhzw8t1qj4k3m.png)
Total surface of the cylinder is given by :
![A=2\pi r h+2\pi r^2\\\\=2287.07+2\pi * (13)^2\\\\=3348.92\ ft^2](https://img.qammunity.org/2022/formulas/mathematics/high-school/3evkh8g87vc1qq91dijsfgtj5vcbpicqzh.png)
The total surface area of the cylinder is not matched with the given data. Hence, option (4) is not correct.