Question: Find the total surface area of a cone with a slant height of $9$ m and a diameter of $16$ m. Use $3.14$ or a calculator button for pi and provide an answer accurate to the nearest hundredth.
1. **State the problem:** We need to find the total surface area of a cone with slant height $l = 9$ m and diameter $d = 16$ m.
2. **Formula for total surface area of a cone:**
$$\text{Total Surface Area} = \pi r^2 + \pi r l$$
where $r$ is the radius and $l$ is the slant height.
3. **Calculate the radius:**
$$r = \frac{d}{2} = \frac{16}{2} = 8 \text{ m}$$
4. **Calculate the base area:**
$$\pi r^2 = 3.14 \times 8^2 = 3.14 \times 64 = 200.96$$
5. **Calculate the lateral surface area:**
$$\pi r l = 3.14 \times 8 \times 9 = 3.14 \times 72 = 226.08$$
6. **Calculate total surface area:**
$$\text{Total Surface Area} = 200.96 + 226.08 = 427.04$$
7. **Final answer:** The total surface area of the cone is $427.04$ square meters, rounded to the nearest hundredth.