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:
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Calculate the area of the base (\( \pi r^2 \)): \[ \pi r^2 = 3.14 \times (10)^2 = 3.14 \times 100 = 314 \text{ square inches} \]
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Calculate the lateral surface area (\( \pi r l \)): \[ \pi r l = 3.14 \times 10 \times 15 = 3.14 \times 150 = 471 \text{ square inches} \]
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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.