Final answer:
The total surface area of the cone is 7π square yards.
Step-by-step explanation:
To find the total surface area of the cone, we need to find the lateral surface area and add it to the base area.
The lateral surface area of a cone is given by the formula πrℓ, where r is the radius and ℓ is the slant height.
In this case, the lateral surface area is 62.8 square yards and the slant height is 2 yards.
So, the lateral surface area of the cone is π(2)(2) = 4π square yards.
The base area of a cone is given by the formula πr^2, where r is the radius.
Since the slant height is given, we can use the Pythagorean theorem to find the radius. The radius is the hypotenuse of a right triangle with the slant height as one of the legs and the height of the cone as the other leg.
Using the Pythagorean theorem, we have r^2 = (2)^2 - (1)^2 = 4 - 1 = 3.
Therefore, the radius is √3 yards.
The base area of the cone is then π(√3)^2 = 3π square yards.
The total surface area of the cone is the sum of the lateral surface area and the base area, 4π + 3π = 7π square yards.