Cones, Cylinders, & Spheres Online Practice

Question

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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

1,256 square inches
1,256 square inches

226.08 square inches
226.08 square inches

480.42 square inches
480.42 square inches

427.04 square inches

Answer 1

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

\[ \text{Surface Area} = \pi r (r + l) \]

where \( r \) is the radius, \( l \) is the slant height, and \( \pi \) is approximately 3.14.

1. Find the radius: The diameter is given as 16 inches, so the radius \( r \) is half of that: \[ r = \frac{16}{2} = 8 \text{ inches} \]

2. Use the slant height: It is given as \( l = 9 \text{ inches} \).

3. Plug the values into the surface area formula: \[ \text{Surface Area} = 3.14 \times 8 \times (8 + 9) \] \[ \text{Surface Area} = 3.14 \times 8 \times 17 \] \[ \text{Surface Area} = 3.14 \times 136 \] \[ \text{Surface Area} \approx 427.04 \text{ square inches} \]

So, the surface area of the cone is approximately 427.04 square inches.

Thus, the correct response is: 427.04 square inches.