To find 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 of the base of the cone,
- \( l \) is the slant height of the cone.
Given:
- The diameter of the cone is 20 inches, so the radius \( r \) is \( \frac{20}{2} = 10 \) inches.
- The slant height \( l \) is 25 inches.
Now, we can substitute the values into the formula.
-
Calculate the area of the base: \[ \pi r^2 = 3.14 \times (10^2) = 3.14 \times 100 = 314 \]
-
Calculate the lateral surface area: \[ \pi r l = 3.14 \times 10 \times 25 = 3.14 \times 250 = 785 \]
-
Add the areas together to get the total surface area: \[ \text{Surface Area} = 314 + 785 = 1099 \]
Therefore, the surface area of the cone is 1099 square inches.
The answer is 1099.