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 ft2900.6 ft2

254.34 ft2254.34 ft2

706.5 ft2706.5 ft2

452.16 ft2

Answer 1

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:

1. Calculate the base area:
\[
\text{Base Area} = \pi r^2 = 3.14 \times (9)^2 = 3.14 \times 81 = 254.34 \, \text{ft}^2
\]

2. Now calculate the lateral surface area:
\[
\text{Lateral Surface Area} = \pi r l = 3.14 \times 9 \times 16 = 3.14 \times 144 = 452.16 \, \text{ft}^2
\]

3. 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**