In a cylinder, consider the following areas:
a) lateral area (THEL)
We can observe the lateral area of a cylinder making its plan:
Thus, the lateral area of the straight cylinder whose height is H and whose radii of the base circles are r is a rectangle of dimensions :
b) base area (THEB): radius circle area r.
c) total area (THET): sum of the lateral area with the base areas.
To get the volume of the cylinder, let's use Cavalieri's principle again. Dice two solids with same height and one plane , if every plan , parallel to the plane , intercepts solids and determines sections of the same area, solids have equal volumes:
If 1 is a rectangle, then V2 = ABH. Thus, the volume of every rectangular parallelepiped and of every cylinder is the product of the base area by the measure of its height:
|Vcylinder = ABH|
In the case of a straight circular cylinder, the base area is the radius circle area. r: . Therefore, its volume is:
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