Volume of the cylinder

The use of geometric figures is actively carried out absolutely in all branches of the national economy, industry, and so on. That is why this subject is studied in such detail in the school curriculum. But not all of us have mastered this interesting science well, so your attention is invited to recall what a cylinder is and how to calculate its volume? That is, before you figure out what the volume of the cylinder is, you need to understand what kind of figure it is. A cylinder is a three-dimensional shape consisting of the following elements: two parallel identical circles (the area of the circles are equal) and the cylinder forming these circles. But there is one condition - the generators of the cylinder and the axis of this must be perpendicular to both circles, that is, one circle is in the literal sense a mirror image of the other.

We described the simplest example - a straight circular cylinder. But in life we can meet not only those, because their diversity is so great that it is almost impossible to describe them all. But let's not go into depth, but consider the most common simple cylinder. So, now that we know what a cylinder is, we can calculate its volume. And what is volume? In other words, you can make a small comparison - this is a kind of capacity of the vessel. From this definition it is clear that such ideal characteristics can not have ideal planar figures, but only three-dimensional ones, which is the cylinder.

Now let's move on to figures and calculations. To find out what the volume of a cylinder is equal to, it is necessary to use the well-known formula by which it is calculated: V = πr² h

Now consider all the values of the formula:

V is the volume of the cylinder;

Π is the Pi number;

R is the radius of the circle;

H is the height of the cylinder.

With the volume of the cylinder, we figured out, the radius of the circle is understandable, but what is the Pi number and the height of the cylinder?

The number Pi is a constant, showing the ratio of the circumference to the length of its diameter. It is considered that it is numerically equal to 3.14. Although in fact this number after the whole part has 10 trillion signs (by calculations for 2011)! But for convenience, we will use the standard size, since we do not need high-precision calculations. Although, for example, the maximum possible number of symbols after space is used in cosmonautics!

The height of the cylinder is the perpendicular distance between its two planes, in our case by circles. The height is the generator of the cylinder. And the most interesting is that the given value is absolutely identical along the entire length of the conjugate circles of the cylinder.

Now that all the variables in the equation are known, the question arises: why is this so? Let us explain this with an example of a parallelepiped. Everyone knows that its volume is equal to the product of its three dimensions: length, width and height. And the area of the base of this figure is equal to the product of length by width, i.e. It turns out that the volume is equal to the product of the base area by the height. And now back to our cylinder, everything is the same: V = Sh, where S is the area of the base of the cylinder, since we have a circle in the base, and the area of the circle is: S = πr².

Now we know how to calculate the volume of a cylinder, but what can it give us? What is the practical application of the acquired knowledge? In everyday life, this knowledge is minimized, for example, you can calculate how much water will fill a cylindrical object, how many loose materials will fit in a cylindrical container. Although we can do without it. But in industry without such knowledge simply can not do. For example, in the manufacture of pipes for various purposes, you can calculate how much liquid or gas they will flow per unit time, etc.