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

1,256 square inches
1,256 square inches

427.04 square inches
427.04 square inches

226.08 square inches

1 answer

To find the surface area of a cone, you 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.

We are 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 plug in the values into the surface area formula.

  1. Calculate the 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. Calculate the lateral surface area:

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

  1. Add the areas together to find the total surface area:

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

Thus, the total surface area of the cone is 427.04 square inches.

The correct response is: 427.04 square inches.