In a cylinder, consider the following areas:

a) lateral area (**THE _{L}**)

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 (**THE _{B}**): radius circle area

**r**.

c) total area (**THE _{T}**): 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 V_{2} = A_{B}H. Thus, the volume of every rectangular parallelepiped and of every cylinder is the product of the base area by the measure of its height:

V_{cylinder} = A_{B}H |

In the case of a straight circular cylinder, the base area is the radius circle area. **r**: . Therefore, its volume is:

Next: Equilateral Cylinder