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This is a two part problem. The first part involves using the given volume and height to determine the radius r.
V = volume of the cone
V = (1/3)pi*r^2*h
480 = (1/3)*3.14*r^2*8
480*3 = 3.14*8*r^2
1440 = 25.12r^2
25.12r^2 = 1440
r^2 = 1440/(25.12)
r^2 = 57.32484076 approximately
r = sqrt(57.32484076)
r = 7.57131697659
r = 7.5713
That's the approximate radius value.
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The second part is where we compute the surface area based on the radius we found, and also the given height.
SA = surface area of the cone
SA = pi*r^2 + pi*r*sqrt(r^2 + h^2)
SA = 3.14*(7.5713)^2 + 3.14*7.5713*sqrt((7.5713)^2 + 8^2)
SA = 441.862415073011
SA = 441.86
The units for the surface area are in square inches, which abbreviates to in^2.