Find the surface area of a cone with diameter 27 m and slant height 19 m. Leave your answer in terms of .
Note: You do not need to include in your answer
To find the surface area of a cone, we need to find the area of the base and the lateral surface area.
First, let's find the radius of the cone. The diameter of the cone is given as 27 m, so we can find the radius by dividing the diameter by 2:
Radius = Diameter / 2 = 27 m / 2 = 13.5 m
Next, let's find the lateral surface area of the cone. The lateral surface area of a cone can be calculated using the formula: Lateral Surface Area = π * radius * slant height
Lateral Surface Area = π * 13.5 m * 19 m = 254.34 m²
Finally, let's find the base area of the cone. The base area of a cone is given by the formula: Base Area = π * radius^2
Base Area = π * (13.5 m)^2 = 572.55 m²
To get the total surface area, we need to add the lateral surface area and the base area:
Total Surface Area = Lateral Surface Area + Base Area = 254.34 m² + 572.55 m² = 826.89 m²
Therefore, the surface area of the cone is 826.89 m².