1. **State the problem:** Find the total surface area of a cone with radius $r=3.78$ m and height $h=2.15$ m. 2. **Formula:** The total surface area $A$ of a cone is given by: $$A = \pi r^2 + \pi r l$$ where $l$ is the slant height. 3. **Find the slant height $l$:** Use the Pythagorean theorem: $$l = \sqrt{r^2 + h^2} = \sqrt{3.78^2 + 2.15^2}$$ Calculate inside the root: $$3.78^2 = 14.2884, \quad 2.15^2 = 4.6225$$ So, $$l = \sqrt{14.2884 + 4.6225} = \sqrt{18.9109} \approx 4.35$$ 4. **Calculate the surface area:** $$A = 3.14 \times 3.78^2 + 3.14 \times 3.78 \times 4.35$$ Calculate each term: $$3.78^2 = 14.2884$$ $$3.14 \times 14.2884 = 44.87$$ $$3.14 \times 3.78 \times 4.35 = 51.63$$ 5. **Add the two parts:** $$A = 44.87 + 51.63 = 96.50$$ 6. **Final answer:** The total surface area of the cone is **96.50 square meters**.