To calculate the surface area of a cone, you need to use the formula:
\[ \text{Surface Area} = \pi r^2 + \pi r l \]
Where:
- \( r \) is the radius of the base of the cone,
- \( l \) is the slant height of the cone,
- \( \pi \) is approximately 3.14.
Given:
- \( r = 10 \) inches
- \( l = 15 \) inches
Step 1: Calculate the area of the base
\[ \text{Area of the base} = \pi r^2 = 3.14 \times (10^2) = 3.14 \times 100 = 314 \text{ square inches} \]
Step 2: Calculate the lateral surface area
\[ \text{Lateral Surface Area} = \pi r l = 3.14 \times 10 \times 15 = 3.14 \times 150 = 471 \text{ square inches} \]
Step 3: Add the areas together
\[ \text{Surface Area} = \text{Area of the base} + \text{Lateral Surface Area} = 314 + 471 = 785 \text{ square inches} \]
Thus, the surface area of the cone is 785 square inches.
The correct response is: 785 square inches.
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