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The barrel is probably much like a cylinder. All surface area is the lateral area+the area of the base(s).
In this case:
SA=(d)("pi")(h)+(2)("pi")(r2)
SA is surface area
d is diameter of the circle base
h is the height
r is the radius of the base
What you are doing with this equation is figuring out the circumference x the height, so you get the area of the tall part. Then you take the area of one of the bases and multiply it by 2.
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