The use of geometric shapes is actively carried out in absolutely all sectors 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 figuring out what a cylinder volume is, you need to understand what kind of figure it is. A cylinder is a three-dimensional figure, consisting of the following elements: two parallel identical circles (the area of ββthe circles are equal) and forming a cylinder connecting these circles. But there is one condition - the generators of the cylinder and the axis of it must be perpendicular to both circles, that is, one circle is literally a mirror image of the other.
We have described the simplest example - a straight circular cylinder. But in life we ββcan meet not only those, because their diversity is so great that it is almost impossible to describe them all. But we will not go deeper, but consider the most ordinary simple cylinder. So, now that we know what a cylinder is, we can calculate its volume. And what is volume? In other words, a small comparison can be made - this is a kind of vessel capacity. From this definition it is clear that ideal flat figures cannot possess such a characteristic, but only three-dimensional, of which the cylinder is.
Now let's move on to numbers and calculations. To find out what the volume of a cylinder is, you must use the well-known formula by which it is calculated: V = ΟrΒ² h
Now consider all the values ββof this formula:
V is the volume of the cylinder;
Ο is the number of Pi;
r is the radius of the circle;
h is the height of the cylinder.
We figured out the volume of the cylinder, 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 of a circle to the length of its diameter. It is commonly believed that numerically it is 3.14. Although in fact this number after the integer part has 10 trillion characters (according to calculations for 2011)! But for convenience, we will use the generally accepted size, since we do not need high-precision calculations at all. Although, for example, in astronautics use the maximum possible number of decimal places!
The height of the cylinder is the perpendicular distance between its two planes, in our case, circles. Height is the generatrix of the cylinder. Moreover, the most interesting is that this value is exactly the same along the entire length of the mating circles of the cylinder.
Now that all the variables in the equation are known, the question arises as to why so? Let us explain this with the example of a box. Everyone knows that its volume is equal to the product of its three dimensions: length, width and height. And the base area of ββthis figure is equal to the product of length and width, i.e. it turns out that the volume is equal to the product of the base area by height. And now back to our cylinder, everything is similar: V = Sh, where S is the area of ββthe base of the cylinder, since we have a circle at the base, and the area of ββthe circle is: S = ΟrΒ².
Now we know how to calculate the volume of a cylinder, but what can it give us? What is the practical application of acquired knowledge? In everyday life, this knowledge is minimized, for example, you can calculate how much water a particular cylindrical object will fill, how many bulk materials will fit in a particular cylindrical container. Although we can do without it. But in industry, one simply cannot do without such knowledge. For example, in the production of pipes for various purposes, you can calculate how much liquid or gas they will let through per unit time, etc.