The formula of a surface area of a cone:
[tex]SA=pi rl+\pi r^2[/tex]
r - radius
l - slant height
We have the diameter d = 6 in and a slant height l = 8 in.
[tex]d=2r\to r=6in:2=3in[/tex]
Substitute:
[tex]SA=\pi(3)(8)+\pi(3^2)=24\pi+9\pi=\boxed{33\pi\ in^2}[/tex]
