Sectional area of a circle
A circle is a locus of points on a plane, the distance from which to its center does not exceed a given number, called the radius of this circle.
A section of a circle is an image of a figure formed by cutting a circle by a plane in the transverse direction.
Formula for calculating the cross-sectional area of a circle:S = π * d 2/ four
d is the diameter of the circle.
You can quickly perform this mathematical operation using our online program. To do this, enter the initial value in the corresponding field and press the button.
This page presents the simplest online calculator for calculating the cross-sectional area of a circle, if the diameter of the circle is known. With this calculator, you can calculate the cross-sectional area of a circle in one click.
How to determine the cross-section of a wire by its diameter? Formula, table.
The diameter of any conductor must match the parameters specified in the documentation that comes with it. But in our time it is, unfortunately, a rarity. For example, if the marking says that the cable - 3 X 2.5 , then its cross-section must be at least 2.5 mm2. But do not be surprised if, after checking, it turns out that the wire is 20-30% less than the stated figure. Therefore, it is better not to be lazy and check the size of the conductor before buying, otherwise it can lead to disastrous consequences.
Determination of wire cross-section by diameter
It is best to use a micrometer or vernier caliper to measure the thickness (diameter) of the wire. Micrometers, whether mechanical or electronic, will show the most accurate result, but the results given by a caliper will do just fine. To measure, you must clean the core from plastic insulation, but not every seller will allow you to do this with the end of the wire on the bay put up for sale. Therefore, it is best to buy a meter of cable and then take measurements. After the data on the diameter of the core are obtained, you can start calculating the cross section.
It is possible to measure the width of the conductor without resorting to precision instruments. Often, a person simply does not have them, and buying such a tool just in order to measure the diameter of a wire once is a waste of money. Therefore, you can resort to another method.
In this case, you will need a screwdriver and a regular ruler to measure. The wire for such a check will have to be stripped thoroughly, by 15 - 20 centimeters. Then the cleaned end of the core is wrapped around the flat rounded metal part of the screwdriver in the manner of a spring, and each subsequent turn must be full and fit snugly against the previous one. The number of turns is not critical, but it would be better to bring them up to 10. This will make it easier to count. The width of the dense 10 turns is measured with a ruler, the result is divided by 10 and, as a result, the diameter of one turn is obtained. You can see an example in the photo below.
A photo is provided at the top where such a "spring" is measured. It is clearly seen that the width of 11 tightly packed turns is 7.5 mm. We take a calculator and divide 7.5 mm by 11. It turns out that the diameter of the tested core is 0.68 mm. Knowing it, you can calculate the cross-section of the wire.
Determine the cross-section of the wire by its diameter using the formula.
It does not matter whether it is a wire or a wire, its shape is invariably round, which means that in cross-section, any core of the cable has the shape of a circle. A cross section is nothing more than the area of a wire's circumference at a cut. And the area of any circle, knowing its diameter (and hence the radius), can be easily found using a simple, familiar to everyone from school, formula: S = πR2 ... "Π" is the number unchanged and always equal to 3.14, "R2" is the radius squared. We substitute the values into the formula, after dividing the diameter by two in order to find out the radius, since in this formula the area is recognized precisely with its help. It turns out: S = 3.14 X 0.342 ... Solving a simple example, we get the figure 0.36. That is, the cross-section of the tested wire is 0.36 mm2. But it is better not to use such a "weak" wire in the power network.
Also, to determine the section, the formula for finding the area of a circle by diameter is also suitable. It looks different: S = π / 4 X D2 ... It is more time consuming, but, one way or another, substituting numbers and solving an example, we get the same result.
Determination of the wire cross-section according to the table.
Going to the store, it will not be superfluous to take with you such a table:
Conductor diameter Conductor cross section 0.8 mm 0.5 mm 20.98 mm 0.75 mm 21.13 mm 1 mm 21.38 mm 1.5 mm 21.6 mm 2.0 mm 21.78 mm 2.5 mm 22.26 mm 4.0 mm 22.76 mm 6.0 mm 23, 57 mm 10.0 mm 24.51 mm 16.0 mm 25.64 mm 25.0 mm2
This will eliminate the need to make unnecessary calculations. Despite the fact that there is a tag on each coil of the cable, which indicates its marking and all its parameters, you should not trust what is written. It would be better to play it safe and measure the diameter of the conductor, and then use the table to roughly estimate what its cross section is.
In particular, the following will be written on the tag: “ VVNG 2х4 ". It follows that in the cable - the number of cores - 2, each of which has a cross section of 4 mm2. To confirm or deny the declared parameters, we measure in one of the ways the diameter of the cable core without insulation. We carry out calculations.
If the section coincides with the one indicated on the tag, you can take it. If the result is much less, you should opt for a more powerful cable, following in parameters, or look in other stores for a better conductor that meets GOST, which is a difficult task nowadays. Stores prefer to buy something cheaper in order to sell it later. And a high-quality cable will not be cheap in any way. Hence the conclusion.
Before you finally decide on a purchase, you need to very carefully inspect the insulation. The plastic sheath of the core must be solid, have an impressive thickness, the same along the entire length. In the event that, in addition to the mismatch in diameter, negative nuances with the braid were also revealed, it is better to look not only for another cable, but also for another store, since, often, all types of cable sold in one place are purchased from the same manufacturer. Therefore, there is no guarantee that, even if you take the cable for a more powerful parameter, its insulation will be better. It's not worth the risk with electricity.
Nevertheless, it is better to overpay, spend more time searching, but buy a high-quality GOST conductor than one produced according to TU. Only in such a case can it be guaranteed that the cable will serve the time stated in the documents without any problems, and, most likely, much longer. It is not worth risking a building just to reduce the search time or save extra pennies. Negligence in cable selection can be disproportionately expensive.
Determination of the cross-section of a stranded wire.
Very often, the cores are composed of many thin wires. How to be in this case? Some "smart guys" twist all the wires into one tight twist, measure it with a caliper and calculate the cross-section using the found diameter.
This is the wrong approach. To measure the cross-section of a stranded conductor, you must measure the diameter of one small wire. Only a micrometer will do here. Having learned the cross-section of one wiring, you should count the number of others, and multiply the cross-section of one by the total number of wires. Only in this case, the cross-section of the stranded wire will have the correct parameters.
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How to calculate the cross-sectional area
When solving problems in geometry, it is necessary to calculate the areas and volumes of figures. If you make a section in any figure, having information about the parameters of the figure itself, you can also find the area of this section. To do this, you need to know special formulas and have spatial thinking.
You will need
- Ruler, pencil, eraser.
The ball is a special case of the simplest three-dimensional figure. Through it you canconduct
an infinite number of sections, and any of them will turn out to be a circle. It will happen no matter how muchclose
the section is located towards the center of the ball. It is easiest to calculate the area of the resulting section if itcarried out
exactly through the center of the ball, the radius of which is known. In this case, the cross-sectional area is: S = πR ^ 2.
Another shape whose cross-sectional area you want to find in geometry problems is a parallelepiped. It has edges and edges. By the edgecalled
one of the planes of a parallelepiped (cube), and an edge is a side. A box whose edges and faces are equal is called a cube. All sections of the cube are squares. Knowing this property, calculate the area of the section-square: S = a ^ 2, where a is the edge of the cube and the side of the section.
of the problem, an ordinary parallelepiped is given, in which all the faces are different, the section can be either a square or a rectangle with different sides. A section drawn parallel to two square faces is a square, and a section drawn parallel to two rectangular faces is a rectangle. If the section passes through the diagonals of the parallelepiped, it is also a rectangle.
multiplying the diagonal of the lower base by the height of the parallelepiped: S = d * h, where d is the diagonal of the base, h is the height of the base.
A cone is one of those shapes of revolution, the sections of which can have different shapes. If you cut the cone parallel to the bottom base, the section will be a circle, and if you cut the section parallel in half through the top of the cone, you will get a triangle. In other cases, the sections will be trapezoidal shapes. If the section is a circle, calculate its area using the following formula: S = πR ^ 2. The area of the section, which is a triangle, is equal to the product of half the base and the height: S = 1 / 2f * h, where f is the base of the triangle, h is the height of the triangle.
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In practice, tasks often arise that require the ability to construct sections of geometric shapes of various shapes and find the area of sections. In this article, we will consider how important sections of a prism, pyramid, cone and cylinder are built, and how to calculate their areas.
It is known from stereometry that a volumetric figure of absolutely any type is limited by a number of surfaces. For example, for polyhedrons such as a prism and a pyramid, these surfaces are the polygonal sides. For a cylinder and a cone, we are already talking about surfaces of revolution of cylindrical and conical figures.
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If we take a plane and cross it in an arbitrary way the surface of a volumetric figure, then we get a section. Its area is equal to the area of the part of the plane that will be inside the volume of the figure. The minimum value of this area is zero, which is realized when the plane touches the figure. For example, a section that is formed by a single point is obtained if the plane passes through the apex of a pyramid or cone. The maximum value of the sectional area depends on the relative position of the figure and the plane, as well as on the shape and size of the figure.
Below we will consider how to calculate the areas of the formed sections for two figures of revolution (a cylinder and a cone) and two polyhedra (a pyramid and a prism).
A circular cylinder is a shape that rotates a rectangle around any of its sides. The cylinder is characterized by two linear parameters: base radius r and height h. Below is a schematic illustration of what a circular straight cylinder looks like.
There are three important section types for this shape:
An elliptical is formed as a result of the intersection of the plane with the lateral surface of the figure at an angle to its base. Circular is the result of the intersection of the cutting plane of the side surface parallel to the base of the cylinder. Finally, rectangular is obtained if the cutting plane is parallel to the axis of the cylinder.
The circular cross-sectional area is calculated by the formula:
S1 = pi * r2
The area of the axial section, that is, rectangular, which passes through the axis of the cylinder, is determined as follows:
S2 = 2 * r * h
A cone is a figure of rotation of a right-angled triangle around one of the legs. The cone has one apex and a round base. Its parameters are also radius r and height h. An example of a cone made from paper is shown below.
There are several types of conic sections. Let's list them:
They replace each other if you increase the angle of inclination of the secant plane relative to the round base. The easiest way to write down the formulas for the cross-sectional area of the round and triangular.
A circular cross-section is formed as a result of the intersection of a conical surface with a plane that is parallel to the base. The following formula is valid for its area:
S1 = pi * r2 * z2 / h2
Here z is the distance from the top of the figure to the formed section. It can be seen that if z = 0, then the plane passes only through the vertex, so the area S1 will be equal to zero. Since z <h, the area of the section under study will always be less than its value for the base.
Triangular is obtained when a plane intersects a shape along its axis of rotation. The shape of the resulting section will be an isosceles triangle, the sides of which are the diameter of the base and two generatrices of the cone. How to find the triangular cross-sectional area? The answer to this question is the following formula:
S2 = r * h
This equality is obtained by applying the formula for the area of an arbitrary triangle in terms of the length of its base and height.
A prism is a large class of figures that are characterized by the presence of two identical polygonal bases, parallel to each other, connected by parallelograms. Any section of a prism is a polygon. In view of the variety of the figures under consideration (inclined, straight, n-angle, regular, concave prisms), the variety of their sections is also great. Below we will consider only some special cases.
If the cutting plane is parallel to the base, then the sectional area of the prism will be equal to the area of this base.
If the plane passes through the geometric centers of the two bases, that is, is parallel to the lateral edges of the figure, then a parallelogram is formed in the section. In the case of straight and regular prisms, the section under consideration will be a rectangle.
A pyramid is another polyhedron that consists of an n-gon and n triangles. An example of a triangular pyramid is shown below.
If the section is carried out parallel to the n-gonal base plane, then its shape will be exactly equal to the shape of the base. The area of such a section is calculated by the formula:
S1 = So * (h-z) 2 / h2
Where z is the distance from the base to the section plane, So is the base area.
If the cutting plane contains the top of the pyramid and intersects its base, then we get a triangular section. To calculate its area, you must refer to the use of the appropriate formula for the triangle.