The surface area of a cone in this case equals the area of the base plus the area of the "body" of the cone.
The area of the base is simple. It is a circle so we use πr².
area: π(6²) = 36π
Now we need the area of the body. This equals the slant height which given times πr.
area: 13.4 × 6π = 80.4π
total area: 36π+80.4π = 365.68
answer: second option