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To find the surface area of a cone, we need to calculate both the lateral surface area and the base area.

The formula for the lateral surface area of a cone is:
\[ \text{Lateral Surface Area} = \pi r l \]
where \( r \) is the radius of the base and \( l \) is the slant height.

The formula for the base area of a cone is:
\[ \text{Base Area} = \pi r^2 \]

Given:
- Radius \( r = 9 \, \text{ft} \)
- Slant height \( l = 12 \, \text{ft} \)

First, calculate the lateral surface area:
\[ \text{Lateral Surface Area} = \pi \times 9 \times 12 = 108\pi \]

Next, calculate the base area:
\[ \text{Base Area} = \pi \times 9^2 = 81\pi \]

Finally, add the lateral surface area and the base area to get the total surface area:
\[ \text{Total Surface Area} = 108\pi + 81\pi = 189\pi \]

Thus, the surface area of the cone is:
\[ \text{Surface Area} = 189\pi \, \text{square feet} \]

If you want the numerical value:
\[ \text{Surface Area} \approx 189 \times 3.1416 = 593.76 \, \text{square feet} \]

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. How do you calculate the volume of this cone?
2. What is the formula for the slant height of a cone if only the height and radius are known?
3. How would the surface area change if the radius were doubled?
4. Can you explain how the lateral surface area of a cone is derived?
5. How do you convert the surface area of the cone into square meters?

Tip: When dealing with cones, always remember that the slant height is different from the vertical height. The slant height is the length of the line segment from the top of the cone to a point on the edge of the base along the cone's surface.

Learn how to calculate the surface area of a cone with a radius of 9 feet and a slant height of 12 feet. Detailed step-by-step solution including the formulas for lateral surface area and base area. Suitable for high school students.

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