At both ends we have two circles each with a radius of 4 in
The area of these = 2 * pi * 4^2 = 32 pi
The lateral suface area ( area of the "side" ) = 2 * pi * radius * height =
2 * pi * 4 * 15 = 120 pi
Putting this all together the surface area = ( 32 + 120) pi ≈ 477.5 in^2