To find the total surface area of the cone, we need to add the lateral surface area to the area of the base. The lateral surface area formula for a cone is π * radius * slant height, and the total surface area includes the base area, which is π * radius^2. Given that the slant height is 2 yards and the lateral surface area is 62.8 square yards, we can find the radius. Let's do the math.
Lateral surface area = π * radius * slant height
62.8 = π * radius * 2
radius = 62.8 / (π * 2)
Now that we have the radius, we can find the total surface area.
Total surface area = π * radius * slant height + π * radius^2
Let's calculate.
