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 of the base,
- \( l \) is the slant height,
- \( \pi \) is approximately 3.14.
Given:
- \( r = 10 \) inches,
- \( l = 15 \) inches.
Let's calculate each part.
- Calculate the area of the base:
\[ \text{Base Area} = \pi r^2 = 3.14 \times (10)^2 = 3.14 \times 100 = 314 \text{ square inches} \]
- 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, add both areas to get 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 785 square inches.