To calculate the surface area of a cone, you can use the following formula:
\[ \text{Surface Area} = \pi r (r + l) \]
where \( r \) is the radius of the base and \( l \) is the slant height.
Given:
- \( r = 9 \) ft
- \( l = 16 \) ft
- \( \pi \approx 3.14 \)
First, calculate the surface area:
-
Calculate the base area: \[ \text{Base Area} = \pi r^2 = 3.14 \times (9)^2 = 3.14 \times 81 = 254.34 , \text{ft}^2 \]
-
Now calculate the lateral surface area: \[ \text{Lateral Surface Area} = \pi r l = 3.14 \times 9 \times 16 = 3.14 \times 144 = 452.16 , \text{ft}^2 \]
-
Now add the base area to the lateral surface area to find the total surface area: \[ \text{Surface Area} = \text{Base Area} + \text{Lateral Surface Area} = 254.34 + 452.16 = 706.5 , \text{ft}^2 \]
Thus, the correct answer is: 706.5 ft²