Question
A cone has a base radius of 9 ft. and a slant height of 16 ft. Which of the following correctly calculates the surface area of the cone? Use π≈3.14
.(1 point)
Responses
254.34 ft.2
254.34 ft. squared
706.5 ft.2
706.5 ft. squared
452.16 ft.2
452.16 ft. squared
900.6 ft.2
900.6 ft. squared
.(1 point)
Responses
254.34 ft.2
254.34 ft. squared
706.5 ft.2
706.5 ft. squared
452.16 ft.2
452.16 ft. squared
900.6 ft.2
900.6 ft. squared
Answers
GPT-4o mini
To find the surface area of a cone, use the 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
- \( \pi \approx 3.14 \)
Now, substitute the values into the formula:
1. Calculate the base area:
\[ \pi r^2 = \pi (9^2) = 3.14 \times 81 = 254.34 \text{ ft}^2 \]
2. Calculate the lateral area:
\[ \pi r l = \pi \times 9 \times 16 = 3.14 \times 144 = 452.16 \text{ ft}^2 \]
3. Add the base area and the lateral area for the total surface area:
\[ \text{Total Surface Area} = \text{Base Area} + \text{Lateral Area} \]
\[ \text{Total Surface Area} = 254.34 + 452.16 = 706.5 \text{ ft}^2 \]
So, the total surface area of the cone is **706.5 ft²**.
The correct response is:
**706.5 ft.²**
\[ \text{Surface Area} = \pi r (r + l) \]
where \( r \) is the radius of the base and \( l \) is the slant height.
Given:
- \( r = 9 \) ft
- \( l = 16 \) ft
- \( \pi \approx 3.14 \)
Now, substitute the values into the formula:
1. Calculate the base area:
\[ \pi r^2 = \pi (9^2) = 3.14 \times 81 = 254.34 \text{ ft}^2 \]
2. Calculate the lateral area:
\[ \pi r l = \pi \times 9 \times 16 = 3.14 \times 144 = 452.16 \text{ ft}^2 \]
3. Add the base area and the lateral area for the total surface area:
\[ \text{Total Surface Area} = \text{Base Area} + \text{Lateral Area} \]
\[ \text{Total Surface Area} = 254.34 + 452.16 = 706.5 \text{ ft}^2 \]
So, the total surface area of the cone is **706.5 ft²**.
The correct response is:
**706.5 ft.²**