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

1 answer

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:

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

  1. Area of the lateral surface:

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

  1. 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.