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Cylinders:
We can derive the formula for finding the surface area of a right circular cylinder
by "slicing" the cylinder open and "unrolling" it to form a rectangle plus two
circular bases. The area of each of circular base is  r 2 . The area of the rectangle is
2 rh , since the length of the rectangle is the circumference of the cylinder. Thus
the total surface area is 2 r 2  2 rh .
Pyramids:
The surface area of a pyramid is obtained by summing the areas of the triangular faces
and the base. The height of each triangular face is called the slat height of the pyramid.
The slant height and the base determine the surface area of a right regular pyramid.
For a right regular pyramid with a base perimeter of P and n sides and slant height l:
Each triangle has a base = P/n
Each triangular face has an area = (1/ 2)( P / n)l
Sum of the areas of the triangular faces = n(1/ 2)( P / n)l  (1/ 2) Pl
Surface area of the pyramid = (1/ 2)Pl + Area of the base
Cones:
The surface area of a right circular cone can be obtained by considering a sequence of
right regular pyramids with increasing number of sides.
The surface area of each side (1/ 2)bl so the lateral surface area is n(1/ 2)bl .
Since the P  nb , the lateral surface area is (1/ 2)Pl . Now as the number of sides
increases ( n   ), P  2 r .
So the lateral surface area  (1/ 2) Pl  (1/ 2)(2 r )l   rl