What is the circumference of a circle knowing the radius. How to find and what will be the circumference of a circle?

Then for a circle, for example: a lid on a tank, a hatch, an umbrella roof, a pit, a rounded ravine, and so on, you can, by measuring the length of the circle, quickly calculate its diameter. To do this, you just need to apply the formula for the circumference of a circle. L = p D Here: L – circumference, n – number Pi equal to 3.14, D – diameter of the circle. Rearrange the required value in the formula for the circumference of the circle to the left and get: D = L/n

Let's look at a practical problem. Suppose you need to make a cover for a round country well, which is currently not accessible. Out of season and unsuitable weather conditions. But you have data on its circumference. Let's assume this is 600 cm. We substitute the values ​​into the indicated formula: D = 600/3.14 = 191.08 cm. So, 191 cm is the diameter of your well. Increase the diameter to 2 meters, taking into account the allowance for the edges. Set the compass to a radius of 1 m (100 cm) and draw a circle.

Helpful advice

It is convenient to draw circles of relatively large diameters at home with a compass, which can be quickly made. It's done like this. Two nails are driven into the lath at a distance from each other equal to the radius of the circle. Drive one nail shallowly into the workpiece. And use the other one, rotating the staff, as a marker.

To calculate the volume of a pipe, measure its length and the inner and outer radii. Determine the cross-sectional areas along the outer and inner radius, calculate the volumes. This will be the internal and external volume of the pipe. After this, calculate the volume of the material from which the pipe is made by simple subtraction. If the material from which the pipe is made is known and it can be weighed, calculate its volume using its density.

You will need

• tape measure, caliper, table of densities of some substances, scales.

Instructions

Determining the volume of a pipe using the geometric method Using a tape measure or any other method, measure the length of the pipe, including all its bends. Then, using a caliper or other suitable device, find the inside diameter of the pipe and calculate the radii by dividing each diameter by 2. Some pipes are marked in inches. To convert this value to , multiply inches by 0.0254. Most often, the internal diameter is indicated in inches. Calculate the total volume of the pipe along the outer radius. To do this, multiply the number 3.14 by the square of the outer radius, measured in meters, and the pipe length V=3.14 R² l, measured in meters. You will get the volume in cubic meters.

Calculate the internal volume of the pipe. Do this in the same way as for the external volume, only when calculating, use the value of the pipe radius V = 3.14 r² l. This way you can determine the volume of substance that can be in the pipe. It could be water, gas, etc. To find the volume of the material from which the pipe is made, subtract the internal volume from the external volume. In order not to make unnecessary calculations, if you do not need to calculate the external and internal volumes, find the volume of the pipe body immediately. To do this, square the difference between the outer and inner radii, multiply by the number 3.14 and the length of the pipe V=3.14 (R-r)² l.

Determining the volume of a pipe body through density Find out from a special table the density of the material from which the pipe is made (steel, cast iron, plastic, glass, etc.) in kg/m³. Then weigh the pipe on a scale, expressing its mass in kilograms. In order to obtain the volume of the pipe body, divide its mass by the density V=m/ρ. You will get the result in cubic meters. In all cases when you need to convert cubic meters to cubic centimeters, multiply the result by 1000000.

A flat geometric figure is called a circle, and the line that bounds it is usually called a circle. The main property of a circle is that every point on this line is at the same distance from the center of the figure. A segment with a beginning at the center of the circle and ending at any point on the circle is called a radius, and a segment connecting two points on the circle and passing through the center is called a diameter.

Instructions

Use Pi to find the length of a diameter given the known circumference. This constant expresses a constant relationship between these two parameters of the circle - regardless of the size of the circle, dividing its circumference by the length of its diameter always gives the same number. It follows from this that to find the length of the diameter, the circumference should be divided by the number Pi. As a rule, for practical calculations of the length of a diameter, accuracy to hundredths of a unit is sufficient, that is, to two decimal places, so the number Pi can be considered equal to 3.14. But since this constant is an irrational number, it has an infinite number of decimal places. If there is a need for a more precise definition, then the required number of digits for pi can be found, for example, at this link - http://www.math.com/tables/constants/pi.htm.

Given the known area of ​​the circle (S), to find the length of the diameter (d), double the square root of the ratio of the area to the number Pi: ​​d=2∗√(S/π).

Given a known side length of a rectangle circumscribed near a circle, the length of the diameter will be equal to this known value.

Given the known lengths of the sides (a and b) of a rectangle inscribed in a circle, the length of the diameter (d) can be calculated by finding the length of the diagonal of this rectangle. Since the diagonal here is the hypotenuse in a right triangle, the legs of which form sides of known length, then according to the Pythagorean theorem, the length of the diagonal, and with it the length of the diameter of the circumscribed circle, can be calculated by finding the square root of the sum of the squares of the lengths of the known sides: d=√( a² + b²).

When performing various jobs, both at home and in production, it may be necessary to determine the diameter of the pipe. You can calculate the diameter of any pipe of the correct shape using simple calculations, which are based on basic knowledge from school geometry.

You will need

• - yardstick;
• - caliper;
• - calculator;
• - a sheet of paper and a pencil.

Instructions

To keep the outer diameter small, use a measuring tool such as a caliper. Spread the jaws of the tool so that its opening is larger than the cross-section of the pipe. Attach the caliper to and squeeze the jaws of the tool so that they tightly cover. Use the scale to determine the diameter of the measured pipe. The caliper ensures pipe measurement accuracy down to tenths of a millimeter.

Use the upper jaws of a caliper to measure the inside diameter of the pipe. Insert the jaws inside the pipe and spread them apart so that the jaws fit snugly against the opposite inner edges of the pipe. Using the measuring scale, determine the internal diameter of the pipe. Please note that a standard caliper can measure pipes with a diameter of up to 150 mm.

If you need to measure the diameter of a pipe without having access to its cut, use a construction tape or thread (depending on the size of the pipe). Using a thread or tape measure, measure the circumference of the pipe (its girth). Then calculate the outer diameter of the pipe using the formula:
D = L / p, where L is the pipe circumference, p = 3.14 (pi).
For example, with a circumference of 400 mm, the outer diameter of the pipe will be:

D = 400 / 3.14 = 127.4 mm.

Calculate the internal diameter of the pipe using the formula:
D’ = D – 2 * t, where D is the outer diameter of the pipe, and t is the wall thickness.
So, for the example discussed above, with a pipe wall thickness of 3 mm, the internal diameter of the pipe will be:

D’ = 127.4 – 2 * 3 = 121.4 mm.

If you have a section of pipe, and the surface area and length of the section are known, then calculate the diameter using the formula for the area of ​​the lateral surface of the cylinder:
D = p * N / S, where N is the length of the pipe, S is the surface area, p = 3.14.

D’ = D – 2 * t, where D is the outer diameter of the pipe, and t is the thickness of its wall.

A segment connecting two divergent points lying on the same circle is called a “chord”, and a chord passing through the center of this circle has another name - “diameter”. Such a chord has the maximum possible length for this circle, which can be calculated in several ways using basic definitions and relationships.

Instructions

The simplest way to determine the diameter (D) of a circle can be used when the radius (R) is known. The radius is a segment connecting the circle with any point lying on the circle. It follows from this that the diameter is made up of two segments, each of which is equal to the radius: D=2*R.

Use a relationship called Pi to calculate the diameter (D) if you know the length of the perimeter (L). The perimeter, in relation to, is usually called the circumference, and Pi expresses the constant relationship between the diameter and the circumference - in Euclidean geometry, dividing the perimeter of a circle by its diameter is always equal to the number Pi. This means that to find the diameter, you need to divide the circumference by this constant: D=L/π.

From the root of the result of dividing the area by Pi and doubling the resulting value: D=2*√(S/π).

If a rectangle is described near a circle and the length of its side is known, then nothing needs to be calculated - such a rectangle can only be a square, and the length of its side will be equal to the diameter of the circle.

In the case of a rectangle inscribed in a circle, the length of the diameter will coincide with the length of its diagonal. To find it, given the known width (H) and height (V) of the rectangle, you can use the Pythagorean theorem, since a triangle formed by the diagonal, width and height will be rectangular. It follows from the theorem that the length of the diagonal of a rectangle, and therefore the diameter of the circle, is equal to the square root of the sum of the squares of the width and height: D= √(H²+V²).

Sources:

• area of ​​a circle through diameter

Calculating the volume of a body is one of the classical problems applied science. Such calculations are often required in engineering activities. To find the volume pipes, it is enough to perform a series of mathematical operations.

You will need

• - Calculator.

Instructions

Measure the internal or external diameter of the pipe, as well as the circumference of the section.

Find the radius of the pipe - R. If you want to calculate the internal volume, you need to find the internal radius. To calculate the volume occupied by a body, you need to calculate the outer radius. Divide the diameter by two. R=D/2. You can also use the section length: R=L/6.28318530. Here L is the circumference and the number is twice Pi.

Calculate the cross-sectional area of ​​the pipe. Square the radius value and multiply it by Pi. The cross-sectional area will be expressed in the same units as the radius value. For example, the radius is represented in centimeters. In this case, the cross-sectional area will be expressed in square centimeters. The formula by which the cross-sectional area is calculated: S = R2*Pi, where S is the required area, and R2 is the radius.

Find the volume of the pipe. To do this, multiply the length of the pipe by its cross-sectional area. Formula: V=S*L, where V is the volume of the pipe, S is the cross-sectional area, L is the length.

Similarly, find the volume of all pipes (if they have different diameters).

note

You must ensure that the pipe length and radius value are expressed in the same units. Otherwise you will get an incorrect value. Usually all calculations are made in centimeters and square centimeters.

Helpful advice

If you use a calculator for calculations, you can store twice the number Pi in its memory. Then it will be possible to quickly calculate the values ​​of several volumes - if you need to find the volume of pipes with different diameters. You can also enter ready-made formulas into the memory of a calculator or computer in order to quickly make the necessary calculations in the future. If you often have to work with mathematical formulas, can be downloaded on the Internet special program.

Sources:

• Internal volume of a linear meter of pipe in liters - table in 2018

When constructing various geometric shapes, it is sometimes necessary to determine their characteristics: length, width, height, and so on. If we are talking about a circle or circle, then we often have to determine its diameter. A diameter is a straight line segment that connects the two points furthest from each other located on a circle.

You will need

• - yardstick;
• - compass;
• - calculator.

Instructions

In the simplest case, determine the diameter using the formula D = 2R, where R is the radius of the circle with the center at point O. This is convenient if you are drawing a circle with a predetermined . For example, if, when constructing a figure, you set the opening of the compass legs to 50 mm, then the diameter of the resulting circle will be equal to twice the radius, that is, 100 mm.

If you know the circumference of a circle that is outer border circle, then use the formula to determine the diameter:

D = L/p, where
L – circumference;
p is the number “pi”, equal to approximately 3.14.

For example, if the length is 180 mm, then the diameter will be approximately: D = 180 / 3.14 = 57.3 mm.

If you have a pre-drawn circle with radius, diameter and circumference, use a compass and a graduated ruler to estimate the diameter. The difficulty is to find two points on the circle that are as far apart as possible, that is, those that will be located exactly on the diameter.

Using a ruler, draw a straight line so that it intersects the circle anywhere. Mark the intersection points of the line and the circle as A and B. Now set the compass opening so that it is more than half of the segment AB.

Place the compass needle at point A and draw an arc intersecting segment AB or even a circle. Now, without changing the solution of the compass, install it at point B and do the same. As a result, you will get the intersection points of two circles on either side of the segment AB. Connect them using a ruler with a straight line so that it intersects the circle at points C and D. The segment CD will be the required diameter.

Now measure the diameter using a measuring ruler, applying it to points C and D. The second way to determine the diameter: first attach the legs of the compass to points C and D, and then transfer the solution of the compass to the measuring scale of the ruler.

Pi is the ratio of the circumference of a circle to its diameter. It follows that the circumference is equal to “pi de” (C = π*D). Based on this relationship, it is easy to derive the formula for the inverse relationship, i.e. D=С/π.

You will need

• - calculator.

Instructions

To find the diameter of a circle, knowing its length, divide the circumference by pi (π), which is approximately three point fourteen (3.14). The diameter value will be obtained in the same units as the circumference. This formula can be written in the following form: D = C/π, where: C is the circumference, π is the number “pi”, approximately equal to 3.14.

To more accurately calculate the diameter of a circle, use a more precise representation of pi, for example: 3.1415926535897932384626433832795. Of course, it is not at all necessary to use all of these numbers; for most engineering calculations, 3.1416 is quite enough.

When calculating the diameter of a circle based on its length, note that on (especially engineering) calculators there is a special key for entering the number “pi”. Such a button is indicated by the inscription on (above, below) it “π” or something similar. For example, in the Windows virtual calculator the corresponding button is designated pi. Using a special key allows you to significantly speed up entering the number “pi” and avoid errors when entering it. In addition, the number “pi” stored in the calculator’s memory is presented there with the highest possible accuracy for each device.

Sometimes measuring the circumference of a circle is the only practical way to know its diameter. This is especially true for pipes and cylindrical structures that “have no beginning or end.”

To measure the circumference (cross section) of a cylindrical object, take a thread or rope of sufficient length and wrap it around the cylinder (in one turn).

If very high measurement accuracy is required or the object has a very small diameter, then wrap the cylinder several times, and then divide the length of the thread (rope) by the number of turns. In proportion to the number of turns, the accuracy of measuring the circumference will increase, and, accordingly, the calculation of its diameter.

Sources:

• circumference knowing the diameter

Many problems in geometry are based on determining the cross-sectional area of ​​a geometric body. One of the most common geometric bodies is a sphere, and determining its cross-sectional area can prepare you for solving problems of the most different levels difficulties.

Instructions

Put in the drawing the conditional parameters indicating the radius of the ball (R), the distance between the cutting plane and the center of the ball (k), the radius of the secant area (r) and the required cross-sectional area (S).

Define the location boundaries of the sectional area as a value ranging from 0 to πR^2. This interval is due to two logical conclusions. - If the distance k is equal to the radius of the cutting plane, the plane can touch the ball at only one point and S is equal to 0. - If the distance k is equal to 0, then the center of the plane coincides with the center of the ball, and the radius of the plane coincides with the radius R. Then S by the formula to calculate the area of ​​a circle πR^2.

Taking it as a fact that the cross-sectional figure of a ball is always a circle, reduce the problem to finding the area of ​​this circle, or more precisely, to finding the radius of the cross-sectional circle. To do this, imagine that all points on the circle are vertices right triangle. As a result, R is the hypotenuse, r is one of the legs. The second leg becomes distance k - a perpendicular segment that connects the cross-sectional circle with the center of the ball.

Considering that the remaining sides of the triangle - leg k and hypotenuse R - are already given, use the Pythagorean theorem. The leg length r is equal to the square root of the expression (R^2 - k^2).

Substitute the found value of r into the formula to calculate the area of ​​the circle πR^2. Thus, the cross-sectional area S is determined by the formula π(R^2 - k^2). This formula will also be true for the boundary points of the area when k = R or k = 0. When substituting these values, the cross-sectional area S is equal to either 0 or the area of ​​a circle with ball radius R.

Video on the topic

The need to determine the diameter of the pipe often arises when replacing sewer pipes, selecting a heated towel rail and other household work. You can determine it yourself; for this you only need a tape measure or caliper.

Let's take a compass. Let’s place the leg of the compass with a needle at point “O”, and rotate the leg of the compass with a pencil around this point. Thus, we will get a closed line. Such a closed line is called - circle.

Let's take a closer look at the circle. Let's figure out what is called the center, radius and diameter of a circle.

• (·)O is called the center of the circle.
• A segment that connects the center and any point on the circle is called radius of the circle. The radius of a circle is designated by the letter "R". In the figure above, this is the segment “OA”.
• A segment that connects two points on a circle and passes through its center is called diameter of the circle.

  The diameter of the circle is designated by the letter “D”. In the figure above, this is the segment “BC”.

  The figure also shows that the diameter is equal to two radii. Therefore, the expression “D = 2R” is valid.

Number π and circumference

Before you figure out how to calculate the circumference of a circle, you need to find out what the number π (read as “Pi”) is, which is so often mentioned in lessons.

In the distant times of mathematics Ancient Greece carefully studied the circle and came to the conclusion that the length of a circle and its diameter are interrelated.

Remember!

The ratio of the circumference of a circle to its diameter is the same for all circles and is denoted by the Greek letter π (“Pi”).
π ≈ 3.14…

The number "Pi" refers to numbers whose exact value cannot be written down using any ordinary fractions, nor using decimals. For our calculations it is enough for us to use the value π,
rounded to the hundredth place π ≈ 3.14…

Now, knowing what the number π is, we can write the formula for the circumference of a circle.

Remember!

Circumference is the product of the number π and the diameter of the circle. The circumference of the circle is indicated by the letter “C” (read as “Tse”).
C= π D
C = 2π R, since D = 2R

How to find the circumference of a circle

To consolidate the knowledge gained, let's solve a problem on a circle.

Vilenkin 6th grade. Number 831

The task:

Find the length of a circle whose radius is 24 cm. Round the number π to the nearest hundredth.

Let's use the formula for circumference:

C = 2π R ≈ 2 3.14 24 ≈ 150.72 cm

Let's analyze the inverse problem, when we know the circumference of a circle, and we are asked to find its diameter.

Vilenkin 6th grade. Number 835

The task:

Determine the diameter of the circle if its length is 56.52 in. (π ≈ 3.14).

Let us express the diameter from the formula for the circumference of a circle.

C= π D
D = C / π
D = 56.52 / 3.14 = 18 dm

Chord and arc of a circle

In the figure below, mark two points on the circle “A” and “B”. These points divide the circle into two parts, each of which is called arc. These are the blue arc "AB" and the black arc "AB". Points "A" and "B" are called the ends of the arcs.

Definition of a circle in the article Circle.

The circumference is calculated from diameter according to the formula::

where r is the radius, d is the diameter of the circle, and π (Greek letter pi), which is a mathematical constant, is the ratio of the circumference of a circle to its diameter (the value of pi, first digits: 3.141,592,653,589,793).

Wikimedia Foundation. 2010.

See what “Circumference” is in other dictionaries:

tank circumference- - Topics oil and gas industry EN tank circumference ...

circumference a set of known operations- - [A.S. Goldberg. English-Russian energy dictionary. 2006] Energy topics in general EN circuit ... Technical Translator's Guide

LENGTH, lengths, plural. no, female The extension of a line, plane, body in the direction in which two extreme points(lines, planes, bodies) lie at the greatest distance from one another. Items are measured in length, width and height. Table length. Measures… … Dictionary Ushakova

length- ы/, only units, w. 1) Extension in the direction in which the two extreme points of a line, plane, or body lie at the greatest distance from each other. Measure of length. Skis are two meters long. Measure the platform in length and width. Synonyms: distance… … Popular dictionary of the Russian language

- (or, what is the same, the arc length of a curve) in metric space is a numerical characteristic of the length of this curve. Historically, calculating the length of a curve was called straightening the curve (from the Latin rectificatio, straightening). If the length of the curve... ... Wikipedia

Scale length- The distance between the extreme marks of the scale, measured along an arc of a circle or along a straight line passing through the middle of the smallest marks

Very often, when solving school assignments in physics or science, the question arises - how to find the circumference of a circle, knowing the diameter? In fact, there are no difficulties in solving this problem; you just need to clearly imagine what formulas,concepts and definitions are required for this.

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Basic concepts and definitions

1. Radius is the line connecting the center of the circle and its arbitrary point. It is denoted by the Latin letter r.
2. A chord is a line connecting two arbitrary points lying on a circle.
3. Diameter is the line connecting two points of a circle and passing through its center. It is denoted by the Latin letter d.
4. is a line consisting of all points located at equal distances from one selected point, called its center. We will denote its length by the Latin letter l.

The area of ​​a circle is the entire territory enclosed within a circle. It is measured in square units and is denoted by the Latin letter s.

Using our definitions, we come to the conclusion that the diameter of a circle is equal to its largest chord.

Attention! From the definition of what the radius of a circle is, you can find out what the diameter of a circle is. These are two radii laid out in opposite directions!

Diameter of a circle.

Finding the circumference and area of ​​a circle

If we are given the radius of a circle, then the diameter of the circle is described by the formula d = 2*r. Thus, to answer the question of how to find the diameter of a circle, knowing its radius, the last one is enough multiply by two.

The formula for the circumference of a circle, expressed in terms of its radius, has the form l = 2*P*r.

Attention! The Latin letter P (Pi) denotes the ratio of the circumference of a circle to its diameter, and this is a non-periodic decimal. In school mathematics, it is considered a previously known tabular value equal to 3.14!

Now let's rewrite the previous formula to find the circumference of a circle through its diameter, remembering what its difference is in relation to the radius. It will turn out: l = 2*P*r = 2*r*P = P*d.

From the mathematics course we know that the formula describing the area of ​​a circle has the form: s = П*r^2.

Now let's rewrite the previous formula to find the area of ​​a circle through its diameter. We get,

s = П*r^2 = П*d^2/4.

One of the most difficult tasks in this topic is determining the area of ​​a circle through the circumference and vice versa. Let's take advantage of the fact that s = П*r^2 and l = 2*П*r. From here we get r = l/(2*П). Let's substitute the resulting expression for the radius into the formula for the area, we get: s = l^2/(4P). In a completely similar way, the circumference is determined through the area of ​​the circle.

Determining radius length and diameter

Important! First of all, let's learn how to measure the diameter. It's very simple - draw any radius, extend it in the opposite direction until it intersects with the arc. We measure the resulting distance with a compass and use any metric tool to find out what we are looking for!

Let us answer the question of how to find out the diameter of a circle, knowing its length. To do this, we express it from the formula l = П*d. We get d = l/P.

We already know how to find its diameter from the circumference of a circle, and we can also find its radius in the same way.

l = 2*P*r, hence r = l/2*P. In general, to find out the radius, it must be expressed in terms of the diameter and vice versa.

Suppose now you need to determine the diameter, knowing the area of ​​the circle. We use the fact that s = П*d^2/4. Let us express d from here. It will work out d^2 = 4*s/P. To determine the diameter itself, you will need to extract square root of the right side. It turns out d = 2*sqrt(s/P).

Solving typical tasks

1. Let's find out how to find the diameter if the circumference is given. Let it be equal to 778.72 kilometers. Required to find d. d = 778.72/3.14 = 248 kilometers. Let's remember what a diameter is and immediately determine the radius; to do this, we divide the value d determined above in half. It will work out r = 248/2 = 124 kilometer
2. Let's consider how to find the length of a given circle, knowing its radius. Let r have a value of 8 dm 7 cm. Let's convert all this into centimeters, then r will be equal to 87 centimeters. Let's use the formula to find the unknown length of a circle. Then our desired value will be equal to l = 2*3.14*87 = 546.36 cm. Let's convert our obtained value into integer numbers of metric quantities l = 546.36 cm = 5 m 4 dm 6 cm 3.6 mm.
3. Let us need to determine the area of ​​a given circle using the formula through its known diameter. Let d = 815 meters. Let's remember the formula for finding the area of ​​a circle. Let's substitute the values ​​given to us here, we get s = 3.14*815^2/4 = 521416.625 sq. m.
4. Now we will learn how to find the area of ​​a circle, knowing the length of its radius. Let the radius be 38 cm. We use the formula known to us. Let us substitute here the value given to us by condition. You get the following: s = 3.14*38^2 = 4534.16 sq. cm.
5. The last task is to determine the area of ​​a circle based on the known circumference. Let l = 47 meters. s = 47^2/(4P) = 2209/12.56 = 175.87 sq. m.

Circumference

A circle consists of many points that are at equal distances from the center. It's flat geometric figure, and finding its length is not difficult. A person encounters a circle and a circle every day, regardless of what field he works in. Many vegetables and fruits, devices and mechanisms, dishes and furniture are round in shape. A circle is the set of points that lies within the boundaries of the circle. Therefore, the length of the figure is equal to the perimeter of the circle.

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Characteristics of the figure

In addition to the fact that the description of the concept of a circle is quite simple, its characteristics are also easy to understand. With their help you can calculate its length. The inner part of the circle consists of many points, among which two - A and B - can be seen at right angles. This segment is called the diameter, it consists of two radii.

Within the circle there are points X such, which does not change and is not equal to unity, the ratio AX/BX. In a circle, this condition must be met; otherwise, this figure does not have the shape of a circle. Each point that makes up a figure is subject to the following rule: the sum of the squared distances from these points to the other two always exceeds half the length of the segment between them.

Basic circle terms

In order to be able to find the length of a figure, you need to know the basic terms relating to it. The main parameters of the figure are diameter, radius and chord. The radius is the segment connecting the center of the circle with any point on its curve. The magnitude of a chord is equal to the distance between two points on the curve of the figure. Diameter - distance between points, passing through the center of the figure.

Basic formulas for calculations

The parameters are used in the formulas for calculating the dimensions of a circle:

Diameter in calculation formulas

In economics and mathematics there is often a need to find the circumference of a circle. But also in Everyday life You may encounter this need, for example, when building a fence around a round pool. How to calculate the circumference of a circle by diameter? In this case, use the formula C = π*D, where C is the desired value, D is the diameter.

For example, the width of the pool is 30 meters, and the fence posts are planned to be placed at a distance of ten meters from it. In this case, the formula for calculating the diameter is: 30+10*2 = 50 meters. The required value (in this example, the length of the fence): 3.14*50 = 157 meters. If the fence posts stand at a distance of three meters from each other, then a total of 52 of them will be needed.

Radius calculations

How to calculate the circumference of a circle from a known radius? To do this, use the formula C = 2*π*r, where C is the length, r is the radius. The radius in a circle is half the diameter, and this rule can be useful in everyday life. For example, in the case of preparing a pie in a sliding form.

To prevent the culinary product from getting dirty, it is necessary to use a decorative wrapper. How to cut a paper circle of the appropriate size?

Those who are a little familiar with mathematics understand that in this case you need to multiply the number π by twice the radius of the shape used. For example, the diameter of the shape is 20 centimeters, respectively, its radius is 10 centimeters. Using these parameters, the required size of the circle is found: 2*10*3, 14 = 62.8 centimeters.

Handy calculation methods

If it is not possible to find the circumference using the formula, then you should use available methods for calculating this value:

• If a round object is small, its length can be found using a rope wrapped around it once.
• The size of a large object is measured as follows: a rope is laid out on a flat surface, and a circle is rolled along it once.
• Modern students and schoolchildren use calculators for calculations. Online, you can find out unknown quantities using known parameters.

Round objects in the history of human life

The first round-shaped product that man invented was the wheel. The first structures were small round logs mounted on an axle. Then came wheels made of wooden spokes and rims. Gradually, metal parts were added to the product to reduce wear. It was in order to find out the length of the metal strips for the wheel upholstery that scientists of past centuries were looking for a formula for calculating this value.

A potter's wheel has the shape of a wheel, most parts in complex mechanisms, designs of water mills and spinning wheels. Round objects are often found in construction - frames of round windows in the Romanesque architectural style, portholes in ships. Architects, engineers, scientists, mechanics and designers every day in their field professional activity are faced with the need to calculate the size of a circle.