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A plane horizontal surface with no depth refers to a flat area on a curved surface.
A flat round object is a circle. Surface area of a circle = pi*radius squared.
The area of the object.
The cylinder only has 2 faces which are flat but the sides are curved.
A cuboid has 6 flat faces but no curved surfaces. ..________ ./............../| /_______/.| |..............|.| |..............|./ |_______|/