Cylinder Area

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.

Cylinder volume

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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