To find the surface area of a cone, we use the formula:
\[ \text{Surface Area} = \pi r^2 + \pi r l \]
where \( r \) is the radius, \( l \) is the slant height, and \( \pi \) is approximately 3.14.
- First, calculate the area of the base:
\[ \pi r^2 = 3.14 \times (10)^2 = 3.14 \times 100 = 314 \text{ square inches} \]
- Next, calculate the lateral surface area:
\[ \pi r l = 3.14 \times 10 \times 15 = 3.14 \times 150 = 471 \text{ square inches} \]
- Finally, add both areas to get the total surface area:
\[ \text{Total Surface Area} = 314 + 471 = 785 \text{ square inches} \]
Thus, the surface area of the cone is 785 square inches.
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