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Area of the top and bottom = \[2 * \Pi * r^2\]
For the cylider height, Take the differential dx of a wall of height y. The number of strips is 2 Pi. The radius is x. The area of the outer wall is \[2 * \Pi * xy dx\]
Area of a cylinder = \[(2 * \Pi * r^ 2) + (2 * \Pi * x * y)\]