Find the lateral surface area and total surface area of the cone that has a radius of 12 ft , slant height of 15 ft , and height of 9 ft .

To find the lateral surface area of a cone, you can use the formula: Lateral Surface Area = π * r * l where r is the radius and l is the slant height. For your cone, using r = 12 ft and l = 15 ft: Lateral Surface Area = π * 12 * 15 = 180π ft², which is approximately 565.49 ft². The total surface area of a cone is calculated with the formula: Total Surface Area = Lateral Surface Area + Base Area Base Area = π * r². So, Base Area = π * (12)² = 144π ft², approximately 452.39 ft². Total Surface Area = 180π + 144π = 324π ft², which is approximately 1016.89 ft². And there you have it—a cone that’s ready to shine with a lateral surface area of about 565.49 ft² and a total surface area of around 1016.89 ft²!