To calculate the surface area of a cone, we can use the formula:
\[ \text{Surface Area} = \pi r^2 + \pi r l \]
where \( r \) is the radius and \( l \) is the slant height.
Given:
- Radius, \( r = 10 \) inches
- Slant height, \( l = 15 \) inches
- Using \( \pi \approx 3.14 \)
We first calculate the base area:
\[ \text{Base Area} = \pi r^2 = 3.14 \times (10)^2 = 3.14 \times 100 = 314 \text{ square inches} \]
Next, we calculate the lateral surface area:
\[ \text{Lateral Surface Area} = \pi r l = 3.14 \times 10 \times 15 = 3.14 \times 150 = 471 \text{ square inches} \]
Now, we add the base area and the lateral surface area to find the total surface area:
\[ \text{Total Surface Area} = \text{Base Area} + \text{Lateral Surface Area} = 314 + 471 = 785 \text{ square inches} \]
Therefore, the surface area of the cone is
\[ \boxed{785} \text{ square inches} \]
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