To find the surface area of a cone, you can use the formula:
\[ \text{Surface Area} = \pi r^2 + \pi r l \]
where:
- \( r \) is the radius,
- \( l \) is the slant height.
In this case, the radius \( r = 10 \) inches and the slant height \( l = 15 \) inches.
-
Calculate the base area (circular area): \[ \pi r^2 = 3.14 \times (10^2) = 3.14 \times 100 = 314 \text{ square inches} \]
-
Calculate the lateral surface area (the area of the cone's side): \[ \pi r l = 3.14 \times 10 \times 15 = 3.14 \times 150 = 471 \text{ square inches} \]
-
Add the two areas together to find the total surface area: \[ \text{Surface Area} = 314 + 471 = 785 \text{ square inches} \]
Thus, the total surface area of the cone is 785 square inches.