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

480.42 square inches
480.42 square inches

226.08 square inches
226.08 square inches

1,256 square inches
1,256 square inches

427.04 square inches

Answer 1

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

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

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

Given:
- Diameter = 16 inches, so radius \( r = \frac{16}{2} = 8 \) inches.
- Slant height \( l = 9 \) inches.
- Use \( \pi \approx 3.14 \).

Calculating the surface area:

1. Area of the base:

\[
\text{Area of the base} = \pi r^2 = 3.14 \times (8^2) = 3.14 \times 64 = 200.96 \text{ square inches}
\]

2. Area of the lateral surface:

\[
\text{Lateral Surface Area} = \pi r l = 3.14 \times 8 \times 9 = 3.14 \times 72 = 226.08 \text{ square inches}
\]

3. Total surface area:

\[
\text{Total Surface Area} = \text{Area of the base} + \text{Lateral Surface Area}
\]
\[
\text{Total Surface Area} = 200.96 + 226.08 = 427.04 \text{ square inches}
\]

Thus, the total surface area of the cone is \( \boxed{427.04} \) square inches.