Lesson 4ª

AREAS OF ROUND SHAPES

Cylinder:
A rectangle which spins around on one of its sides generates, produces, or creates a cylinder:

The rectangle of the figure above spins around on axis AB on one of its longer sides. The parallel side, as the rectangle spins, creates or generates a cylinder in the direction shown by green arrows.
The side generated by the shape is called a generatrix.

To create a cylinder, we need two circles and one rectangle, whose length equals the length of the circumference of any of the two bases:

In the figure above, you can see two circles with a radius r and a rectangle, whose length is equal to the circumference which surrounds one of the circles, in other words,  and its height is the value of the generatrix or one of the sides of the rectangle with longer length.
Its side area equals its base perimeter (length of the circumference), which will be the base of the rectangle, times the measurement of its height or generatrix.
We will call the perimeter P, we will call the height h or generatrix

The total area equals the side area plus the area of the two bases, which are 2 equal circles.

15(4).12  A cylinder has a circle base with a radius of 2 cm and a height of 4 cm. Which is its side area? its total area?