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 900.6 ft2 900.6 ft2 254.34 ft2 254.34 ft2 452.16 ft2 452.16 ft2 706.5 ft2
Answers
GPT-4o mini
To calculate the surface area of a cone, we can use the formula:
\[
\text{Surface Area} = \pi r^2 + \pi r l
\]
where \( r \) is the base radius, \( l \) is the slant height, and the term \( \pi r^2 \) represents the area of the base, while \( \pi r l \) represents the lateral surface area.
Given:
- Base radius \( r = 9 \) ft
- Slant height \( l = 16 \) ft
- Using \( \pi \approx 3.14 \)
Now we can calculate:
1. Calculate the area of the base:
\[
\pi r^2 = 3.14 \times (9^2) = 3.14 \times 81 = 254.34 \, \text{ft}^2
\]
2. Calculate the lateral surface area:
\[
\pi r l = 3.14 \times 9 \times 16 = 3.14 \times 144 = 452.16 \, \text{ft}^2
\]
3. Add the two areas together to find the total surface area:
\[
\text{Surface Area} = 254.34 + 452.16 = 706.5 \, \text{ft}^2
\]
Thus, the correct calculation for the surface area of the cone is:
\[
\boxed{706.5 \, \text{ft}^2}
\]
\[
\text{Surface Area} = \pi r^2 + \pi r l
\]
where \( r \) is the base radius, \( l \) is the slant height, and the term \( \pi r^2 \) represents the area of the base, while \( \pi r l \) represents the lateral surface area.
Given:
- Base radius \( r = 9 \) ft
- Slant height \( l = 16 \) ft
- Using \( \pi \approx 3.14 \)
Now we can calculate:
1. Calculate the area of the base:
\[
\pi r^2 = 3.14 \times (9^2) = 3.14 \times 81 = 254.34 \, \text{ft}^2
\]
2. Calculate the lateral surface area:
\[
\pi r l = 3.14 \times 9 \times 16 = 3.14 \times 144 = 452.16 \, \text{ft}^2
\]
3. Add the two areas together to find the total surface area:
\[
\text{Surface Area} = 254.34 + 452.16 = 706.5 \, \text{ft}^2
\]
Thus, the correct calculation for the surface area of the cone is:
\[
\boxed{706.5 \, \text{ft}^2}
\]