1. **State the problem:** We need to find the total surface area of a cylinder with height $h=7$ m and radius $r=4$ m. 2. **Formula for total surface area of a cylinder:** $$\text{Total Surface Area} = 2\pi r^2 + 2\pi rh$$ This formula includes the areas of the two circular bases ($2\pi r^2$) and the curved surface area ($2\pi rh$). 3. **Substitute the given values:** $$2\pi (4)^2 + 2\pi (4)(7)$$ 4. **Calculate each part:** $$2\pi \times 16 + 2\pi \times 28$$ 5. **Simplify:** $$32\pi + 56\pi$$ 6. **Add the terms:** $$88\pi$$ **Final answer:** The total surface area of the cylinder is $88\pi$ square meters.