Surface Area of Cones Quick Check

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Question
What is the surface area, in square inches, of a cone with a radius of 10 inches and a slant height of 15 inches? Use 3.14 for pi.(1 point)
Responses

1,177.5 square inches
1,177.5 square inches

471 square inches
471 square inches

785 square inches
785 square inches

2,198 square inches

1 answer

To calculate the surface area \( S \) of a cone, you can use the formula:

\[ S = \pi r^2 + \pi r l \]

where:

  • \( r \) is the radius of the base,
  • \( l \) is the slant height,
  • \( \pi \) is approximately 3.14.

Given:

  • \( r = 10 \) inches
  • \( l = 15 \) inches
  • \( \pi \approx 3.14 \)

Now, plug the values into the formula:

  1. Calculate the area of the base (\( \pi r^2 \)): \[ \pi r^2 = 3.14 \times (10)^2 = 3.14 \times 100 = 314 \text{ square inches} \]

  2. Calculate the lateral surface area (\( \pi r l \)): \[ \pi r l = 3.14 \times 10 \times 15 = 3.14 \times 150 = 471 \text{ square inches} \]

  3. Add the two areas together: \[ S = 314 + 471 = 785 \text{ square inches} \]

Therefore, the surface area of the cone is 785 square inches.

The correct response to your question is: 785 square inches.