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To find the surface area of the cone, we need to use the formula:
Surface Area = πr(r + l)
Given that the radius (r) is 6 and the hypotenuse (l) is 11, we can substitute these values into the formula:
Surface Area = 3.14(6)(6 + 11)
Surface Area = 3.14(6)(17)
Surface Area ≈ 319.56
Rounding to the nearest tenth, the surface area of the cone is approximately 319.6 square units.