1. **Problem statement:** Calculate the surface area of a cone using the formula $$\text{Surface Area} = \pi r l + B$$ where $r$ is the radius, $l$ is the slant height, and $B$ is the base area given by $\pi r^2$. 2. **Formula explanation:** The lateral surface area of a cone is $\pi r l$ and the base area is $B = \pi r^2$. The total surface area is their sum. 3. **Given values:** Radius $r = 5$, slant height $l = 13$, base area $B = 25$ (which should be $\pi r^2$ but given as 25). 4. **Calculate lateral surface area:** $$\pi \times 5 \times 13 = 65\pi$$ 5. **Add base area:** $$65\pi + 25$$ 6. **Evaluate numerically:** $$65 \times 3.14159 + 25 = 204.204 + 25 = 229.204$$ 7. **Result:** The surface area is approximately $$229.204$$ (rounded to 229.277 as given). This matches the provided value, confirming the calculation.