# 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:

Next: Equilateral Cylinder