Formulas for cutting a cylinder. Cylinder: barrel surface area. Formula for a flat barrel surface of a cylinder

The body of the wrapper that is produced at the school is a cylinder, a cone and a core.

Since in the problem on EDI in mathematics you need to solve the problem of the cone and the area of the sphere - respect what has been spared.

Draw up formulas for the volume and flat surface of a cylinder, cone and coolant. Our table has all the stench. Just remember. This is where the knowledge of stereometry begins.

Sometimes it’s bad to paint the appearance of an animal. Or, as per this task, – from below.

2. How many times has the circumference of a cone described by a regular quadrant pyramid been larger than that of a cone inscribed in that pyramid?

It’s simple – just a glimpse of the view from below. Bachimo, the radius of the larger stake is several times greater than the radius of the smaller one. The heights of both cones are the same. Well, the size of a larger cone will be much larger.

Another important moment. We remember that in the problems of Part B of mathematics, the answer is written in the form of a whole number or a final tenth fraction. This is not to blame for any of your species. There is also no need to substitute numbers close to each other! It's bound to speed up! For this purpose, in some tasks the task is formulated, for example, like this: “Find the area of the barrel surface of the cylinder divided by.”

Where else can the formula for volume and flat surface of body wrapping be established? Of course, problem C2 (16). We still know about her.

A cylinder is a figure that is made up of a cylindrical surface and two cylinders drawn out in parallel. The structure of a flat cylinder is a task of the geometric branch of mathematics, which can be done simply. There are a number of different methods, which eventually come down to one formula.

How to find the area of a cylinder - calculation rules

To determine the area of the cylinder, you need two flat bases with a flat side surface: S = Side. + 2Sbas. In the larger version, the formula looks like this: S = 2 π rh + 2 π r2 = 2 π r (h + r).
The area of the side surface of this geometric body can be varied depending on its height and radius of the stake that underlies it. In this case, you can express the radius from the dove of the stake, as it is given. The height can be found if the hardness value is set in the mind. Whose appearance has the same height as before. The formula for the barrel surface of this body looks like this: S = 2 π rh.
The area of the base is taken into account by the formula for finding the area of the stake: S osn = π r 2 . In some places you may not be given a radius, but you may be asked for a dovzhin stake. With this formula, the radius can be easily expressed. С=2π r, r=С/2π. It is necessary to remember that the radius is half the diameter.
With the addition of all these divisions, the number π must not be translated into 3.14159... It is necessary to simply add instructions from the numerical values that were removed as a result of the calculation.
Then you just need to multiply the found area of the base by 2 and add to the resulting number to calculate the area of the side surface of the figure.
If it is indicated that the cylinder has an axial strut and is rectilinear, then the solution will be slightly different. In this type, the width of the rectum will be the diameter of the stake that lies at the base of the body. The maximum figure is equal to the height of the cylinder. It is necessary to select the required values and provide the formula. In this case, the width of the rectangle needs to be divided by two in order to know the area of the base. To find the barrel surface, the dovzhin is multiplied by two radii and by the number π.
You can calculate the area of a given geometric body through its volume. For this, you need to enter the missing value using the formula V = π r 2 h.
There is nothing foldable about the flat cylinder. It is necessary to know the formulas and then deduce from them the values necessary for carrying out the divisions.

A cylinder (from the Greek language, from the words “forge”, “roller”) is a geometric body surrounded by a surface, which is called cylindrical, and two planes. These planes overlap the surface of the figure and are parallel to one another.

A cylindrical surface is a surface that is traced by a straight line in space. These arms are such that the point of the straight line is visible, the flow of the arm is then a curve of a flat type. Such a straight line is called a solid line, and a curved line is called a straight line.

The cylinder is formed from a pair of bases and a barrel cylindrical surface. There are several types of cylinders:

1. Circular, straight cylinder. Such a cylinder has a base and a guide perpendicular to the closing line, and

2. Poor cylinder. There is no straight line between the solid line and the base.

3. Cylinder of a different shape. Hyperbolic, eliptic, parabolic and others.

The area of the cylinder, as well as the area of the entire surface of any cylinder, is determined by the additional folding area of the bases of this figure and the area of the side surface.

The formula that calculates the area of the cylinder for a circular, straight cylinder:

Sp = 2п Rh + 2п R2 = 2п R (h + R).

The area of the barrel surface is slightly more folded, the lower area of the cylinder as a whole, it is calculated by the way of multiplying the closing line to the perimeter of the cut, created by the plane, which is perpendicular to the closing line ii.

The size of the cylinder for a circular or straight cylinder is determined by the size of the object.

The rosette is a rectangular plant with a height of h and a height of P, which is equal to the perimeter of the base.

The result is that the actual area of the cylinder is equal to the area of the flare and can be calculated using the given formula:

If we take a circular, straight cylinder, then for this:

P = 2p R, and Sb = 2p Rh.

If the cylinder is thin, then the area of the barrel surface must increase the length of its cutting line and the perimeter of the cut, which is perpendicular to this cutting line.

Unfortunately, there is no simple formula for expressing the flat barrel surface of a thin cylinder through its height and parameters of its base.

To calculate the cylinder, you need to know a number of facts. Since the cross-section crosses the base with its flatness, such a cut is always straight. All the upright cutlets will be different, depending on the position of the webbing. One side of the axial cut of the figure, which is perpendicular to the base, is the same height, and the other is the diameter of the cylinder base. And the area of such a cut, apparently, is the addition of one side of the rectum to the other, perpendicular to the first, or the addition of the height of this figure to the diameter of its base.

If the crosspieces are perpendicular to the base of the figure, but do not pass through the entire wrap, then the area will be cut to the same height as the cylinder and the chord. To remove the chord, you will need to draw a radius around the base of the cylinder and place it on a new surface on which the crossbar is located. And from this point you need to draw perpendiculars to the radius of the crossbar with the stake. The points of the cross will connect from the center. And the basis of the trikutnik - tse shukana, which is supposed to sound like this: “The sum of the squares of two legs is the ancient hypotenuse, the sum of the square”:

C2 = A2 + B2.

Since the crossbar does not stick out to the base of the cylinder, and the cylinder itself is circular and straight, then the area of the cut is similar to the area of the stake.

The area of the stake is ancient:

S env. = 2п R2.

To know R, you need to divide the dovzhin C by 2p:

R = C \ 2п, where n is the number pi, mathematically constant, calculated for work with the data of the stake and is equal to 3.14.

As stereometry progresses, one of the main themes is “Cylinder”. The area of the barrel surface is taken into account either by the head or by an important formula under the hour of achieving geometrical tasks. However, it is important to remember and remember, which will help you understand the applications and proof of various theorems.

Concept of cylinder

First look at the trace from the beginning. Only after these changes can you begin to look at the formula for the flat surface of the cylinder. Based on this record, other calculations can be calculated.

Under the cylindrical surface there is a surface that is described as solid, which collapses and loses its parallel to a given straight line, which goes along a clear curve.
And another meaning: the cylindrical surface is created without parallel straight lines to move the given curve.
The height of the cylinder is called the height of the cylinder. When the axis is moved to pass through the center of the base, a designated geometric body emerges.
Under everything, they must respect the right thing to go through the insults of the figure.
A cylinder is a stereometric body surrounded by a side surface that moves and two parallel planes.

There are different types of volumetric figures:

Under the circle, a cylinder is hovering on the surface, literally some kind of cylinder. Yogo head warehouses respect the radius of the base and the surface. The height of the figure remains the same.
It is based on a straight cylinder. Its name is removed due to the perpendicularity of the figure, which is reduced to the basics.
The third look is a beveled cylinder. In the case of hand guards, you can use something else called “a circular cylinder with a beveled base.” This figure is determined by the radius of the base, minimum and maximum height.
Under an equal-sided cylinder there is a body whose height and diameter of the round surface are equal.

Washbasin designated

Traditionally, the main “components” of a cylinder are called:

The radius of the base is R (it replaces a similar value of the stereometric figure).
Utvoruvalna - L.
Height – H.
Base area – S base (otherwise apparently, it is necessary to know the stake parameter).
The heights of the beveled cylinder are h 1, h 2 (minimum and maximum).
The area of the barrel surface is S side (if it is flared, it will look like a kind of straight cutter).
The volume of the stereometric figure is V.
Surface area – S.

“Components” of a stereometric figure

When a cylinder rotates, the area of the barrel surface plays an important role. This is due to the fact that this formula includes many other, more complex ones. Therefore, it is necessary to be well grounded in theory.

The main warehouse figures are:

Bichna surface. Apparently, there is a roar out there, which I create according to the instructions of the crooked one.
The full surface includes the main supports and the butt plate.
The crossbar of the cylinder, as a rule, is a straight cutter, which extends parallel to the axis of the figure. Otherwise called a flat. It appears that the same width is behind the warehouse and other figures. So, mentally, the cut is resolved with dovzhins. Width – parallel chords of a stereometric figure.
Under the axle webbing, there is a growing area through the center of the body.
I have decided on the final designation. The auxiliary is the surface that passes through the cylinder seal and is located under the direct cut to the axial cut. With this, one mind can become victorious. The solid surface is designed to fit into the plane of the axial cross-section.

Basic formulas for robots with a cylinder

In order to respond to nutrition and to know the surface area of the cylinder, it is necessary to calculate the main “components” of the stereometric figure and the formula for their determination.

These formulas are subdivided in that expressions are given for a beveled cylinder, and then for a straight one.

Applications with different solutions

It is necessary to determine the area of the barrel surface of the cylinder. Given the diagonal of the cut AC = 8 cm (and it is axial). Exit when closed< ACD = 30°

Decision. The fragments of different sizes are diagonal either way, then in this form:

CD = AC * cos 30°.

Comment. Tricutnik ACD, in a specific butt, straight cut. This means that the part under the CD and AC = cosine of the apparent cut. The values of trigonometric functions can be found in a special table.

Similarly, you can find out the AD values:

AD = AC*sin 30°

Now it is necessary to calculate the required result in the following formulas: the area of the barrel surface of the cylinder is equal to the second result of multiplying n, the radius of the figure and its height. The speed is calculated using a different formula: the area of the cylinder base. This is equivalent to the result of multiplying pi by the square of the radius. I, find the remaining formula: surface area. That's the same amount as the front two areas.

Given the cylinders. Ix volume = 128*p cm³. Which cylinder has the least surface area?

Decision. To start, you need to quickly use formulas to find the volume of a figure and its height.

With respect to the total surface area of the cylinder, according to the theory, it is necessary to formulate its formula.

If we consider the formula as a function of the area of the cylinder, then the minimum “indicator” will be reached at the extremum point. To obtain the remaining meaning, it is necessary to quickly differentiate.

Formulas can be found in a special table for finding similar formulas. Once found, the result is equal to zero and the solution is equal.

Proof: S min will be reached at h = 1/32 cm, R = 64 cm.

A stereometric figure is given - a cylinder and a cross-section. The remainder is carried out in such a manner that it extends parallel to the axis of the stereometric body. The cylinder has the following parameters: BK = 17 cm, h = 15 cm, R = 5 cm. It is necessary to know the distance between the crossbar and the whole.

The fragments under the cylinder webbing are understood to be VSKM, then a straight cutter, the other side of the VM = h. It is necessary to take a look at the VMC. Orthocutaneous tricutaneum. Outgoing from this stronghold, one can see correctly the assumption that MK = ND.

VK² = VM² + MK²

MK² = VK² - VM²

MK² = 17² - 15²

Here you can go without any doubt, so that MK = BC = 8 div.

The offensive cut is a cut through the base of the figure. It is necessary to look at the plain that emerged.

AD – diameter of a stereometric figure. This is parallel to the cut that was guessed in the dark.

BC – straight, spread on the plain of an obvious upright plant.

ABCD – trapezoid. In a particular episode, the isofemoral joint is respected, and the fragments around it are described in a circle.

Once you know the height of the cut trapezoid, you can remove the connection, placing it on the cob. And the same thing: finding the line between everything and carrying out the crossing.

Therefore, it is necessary to calculate the values of AD and OS.

Proof: the cut is expanded 3 cm from the axis.

Instructions for securing the material

Danish cylinder. The area of the barrel surface is determined further. View other parameters. The area of the base is Q, the area of the axial cross-section is M. It is necessary to know S. In other words, the area of the cylinder.

Danish cylinder. The area of the barrel surface must be known at one stage of the task. It appears that height = 4 cm, radius = 2 cm. It is necessary to find out the area of the stereometric figure.

A geometric body, surrounded by two parallel planes and a cylindrical surface.

The cylinder is folded from a barrel surface and two supports. The formula for a flat surface of the cylinder includes a series of developments of the flat base and the butt surface. So, since the bases in the cylinder are equal, then the entire area is covered by the formula:

We will take a look at the layout of a flat cylinder after we know all the necessary formulas. To begin with, we need the formula for the area of the cylinder base. The fragments of the base of the cylinder are round, then we will need to harden:
We remember that in these structures the constant number Π = 3.1415926 is determined, which is covered as a result of reaching the stake up to its diameter. This is a mathematical constant. The butt is laid out flat on the base of the cylinder and we will also look at it a little later.

Area of the barrel surface of the cylinder

The formula of the flat barrel surface of the cylinder is the solid base at its height:

And now let’s take a look at the area in which we will need to re-open the area of the cylinder. The given figure has a height of h = 4 cm, r = 2 cm. We again know the area of the cylinder.
To open the cob, I’ll flatten the base:
Now let's take a look at the layout of the flat barrel surface of the cylinder. With an inflamed look, he has an upright appearance. This area will be filled with the formula that has been put in place. Let’s put all the data before it:
The total area of the stake is the sum of the surface area of the base and the bottom:

Thus, vicoristic formulas for the surface area of the base and the barrel surface of the figure were able to determine the surface area of the cylinder.
The axial cut of the cylinder is straight, in which direction the height and diameter of the cylinder are equal.