Final answer:
The surface area of the cone is approximately 348.51 square units.
Step-by-step explanation:
To find the surface area of a cone, you need to know the radius (r) and the height (h). The formula for the surface area of a cone is:
A = πr(r + √(r² + h²))
Substituting in the given values:
A = 3.14(6(6 + √(6² + 11²)))
A = 3.14(6(6 + √(36 + 121)))
A = 3.14(6(6 + √(157)))
A = 3.14(6(6 + 12.53))
A = 3.14(6(18.53))
A = 3.14(111.18)
A ≈ 348.51
Therefore, the surface area of the cone is approximately 348.51 square units.