Question

Find the surface area of a cone with a diameter of 16 inches and a slant height of 9 inches. Use 3.14 for pi.(1 point)
Responses

427.04 square inches
427.04 square inches

1,256 square inches
1,256 square inches

480.42 square inches
480.42 square inches

226.08 square inches

Answer 1

To find the surface area of a cone, we use the following formula:

\[
\text{Surface Area} = \pi r l + \pi r^2
\]

where:
- \( r \) is the radius of the cone,
- \( l \) is the slant height of the cone,
- \( \pi \) is approximately 3.14.

Given:
- The diameter of the cone is 16 inches, so the radius \( r \) is:
\[
r = \frac{16}{2} = 8 \text{ inches}
\]
- The slant height \( l \) is 9 inches.

Now, we can calculate the surface area by substituting the values into the formula:

1. Calculate the lateral surface area:
\[
\pi r l = 3.14 \times 8 \times 9 = 226.08 \text{ square inches}
\]

2. Calculate the base area:
\[
\pi r^2 = 3.14 \times 8^2 = 3.14 \times 64 = 200.96 \text{ square inches}
\]

3. Add the lateral surface area and the base area to find the total surface area:
\[
\text{Surface Area} = 226.08 + 200.96 = 427.04 \text{ square inches}
\]

Therefore, the surface area of the cone is **427.04 square inches**.