Final answer:
To find the surface area of the right cone with a diameter of 11.2 feet and a height of 9.2 feet, calculate the base area and the lateral area. The surface area is the sum of the base area and the lateral area.
Step-by-step explanation:
To find the surface area of the right cone, we need to calculate the base area and the lateral area.
The base area is given by A = πr², where r is the radius. Since the diameter is given as 11.2 feet, the radius is half of that, so r = 11.2/2 = 5.6 feet.
The lateral area can be found using the formula L = πrl, where l is the slant height. The slant height can be found using the Pythagorean theorem: l = √(h² + r²), where h is the height. Plugging in the values: l = √((9.2)² + (5.6)²) = √(84.64 + 31.36) = √116 = 10.77 feet.
Finally, the surface area of the cone is given by S = A + L = πr² + πrl = π(r² + rl) = 3.14(5.6² + 5.6(10.77)) = 3.14(31.36 + 60.31) = 3.14(91.67) = 287.68 square feet.