As figure has an area of 64 squared units which describes the area of the figure after a dialation with a scale factor of 3 over
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Parameterize the lateral face 
of the cylinder by
where
and 
, and parameterize the disks 
as
where
and 
.
The integral along the surface of the cylinder (with outward/positive orientation) is then
where
where
The integral along the surface of the cylinder (with outward/positive orientation) is then