The diameter is given which is 13.5feet and radius is half of diameter. Therefore radius = 6.75 feet.
Slant height = 16.8 feet
The formula of surface area of cone is
[tex] S = \pi *r(r+l)
\\
S = \pi*6.75(6.75+16.8)
\\
S =\pi*6.75*23.55 = 499.2 ft^2 [/tex]
Correct option is C