## Cylinder

A cylinder is taken to mean a finite section of a right circular
cylinder with its ends closed to form two circular surfaces, as in the
figure above. If the cylinder has a radius *r* and length (height) *h*, then its
volume is given by

V = πr^{2}h

and its surface area is:

- Area of the top is π
*r*^{2} - Area of the bottom is π
*r*^{2} - Area of the side is 2π
*r**h*

Therefore without the top or bottom, the surface area is

*A*= 2π*r**h*

With the top and bottom, the surface area is

*A*= 2π*r*2π^{2}+*r**h =*2π*r*(*r**+ h*)

For a given volume, the cylinder with the smallest surface area has *h*
= 2*r*. For a given surface area, the cylinder with the largest volume has
*h* = 2*r*, (i.e. cylinder fits in a cube (height = diameter.)

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