What is the length of the diameter of a circle. Calculating the radius: how to find the circumference of a circle knowing the diameter. Determining diameter at home

Very often when deciding school assignments in physics, 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.

Basic concepts and definitions

1. Radius is the line connecting the center of the circle and its arbitrary point. It is designated 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 V 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 pre-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 exactly the same 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 instrument 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 unknown length 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

We are surrounded by many objects. And many of them are round in shape. It is given to them for convenient use. Take, for example, a wheel. If it were made in the shape of a square, how would it roll along the road?

In order to make a round object, you need to know what the formula for circumference through diameter looks like. To do this, we first define what this concept is.

Circle and circumference

A circle is a set of points that are located at equal distances from the main point - the center. This distance is called the radius.

The distance between two points on a given line is called a chord. In addition, if a chord passes through the main point (center), then it is called a diameter.

Now let's look at what a circle is. The set of all points that are inside the outline is called a circle.

What is circumference?

After we have covered all the definitions, we can calculate the diameter of a circle. The formula will be discussed a little later.

First, we will try to measure the length of the outline of the glass. To do this, we will wrap it with thread, then measure it with a ruler and find out the approximate length of the imaginary line around the glass. Because the size depends on correct measurement subject, and this method is not reliable. But nevertheless, it is quite possible to make accurate measurements.

To do this, let us again remember the wheel. We have seen repeatedly that if you increase the spoke in a wheel (radius), the length of the wheel rim (circumference) will also increase. And also, as the radius of the circle decreases, the length of the rim also decreases.

If we carefully follow these changes, we will see that the length of an imaginary circular line is proportional to its radius. And this number is constant. Next, let's look at how the diameter of a circle is determined: the formula for this will be used in the example below. And let's look at it step by step.

Circle formula through diameter

Since the length of the outline is proportional to the radius, it is correspondingly proportional to the diameter. Therefore, we will conventionally denote its length by the letter C, and its diameter by d. Since the ratio of the length of the outline and the diameter is a constant number, it can be determined.

Having done all the calculations, we will determine a number that is approximately equal to 3.1415... For the reason that during the calculations a specific number did not work out, we will denote it with the letter π . This icon will be useful to us in order to derive the formula for the circumference of a circle through its diameter.

Let's draw an imaginary line through the central point and measure the distance between the two extreme ones. This will be the diameter. If we know the diameter of a circle, the formula for determining its length will look like this: C = d * π.

If we determine the length of different outlines, then if their diameter is known, the same formula will be applied. Because the sign π - this is an approximate calculation, it was decided to multiply the diameter by 3.14 (a number rounded to hundredths).

How to calculate diameter: formula

This time, let's try using this formula to calculate other quantities besides the length of the outline. To calculate the diameter from the circumference, the same formula is used. Only for this purpose we divide its length by π . It will look like this d = C / π.

Let's look at how this formula works in practice. For example, we know the length of the outline of a well, we need to calculate its diameter. It is impossible to measure it because there is no access to it due to weather conditions. Our task is to make a lid. What should we do in this case?

You need to use the formula. Let's take the length of the well outline - for example, 600 cm. We put a specific number in the formula, namely C = 600 / 3.14. As a result, we get approximately 191 cm. Let's round the result to 200 cm. Then, using a compass, draw a round line with a radius of 100 cm.

Since an outline with a large diameter must be drawn with an appropriate compass, you can make such a tool yourself. To do this, take a strip of the required length and drive a nail at each end. We install one nail into the workpiece and drive it in lightly so that it does not move from the intended place. And with the help of the second we draw a line. The device is very simple and convenient.

Modern technologies allow you to use an online calculator to calculate the length of the outline. To do this, you just need to enter the diameter of the circle. The formula will be applied automatically. You can also calculate the circumference of a circle using the radius. Also, if you know the circumference of a circle, the online calculator calculates the radius and diameter using this formula.

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 the circumference. L = n DHere: 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 side 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 accessible in at the moment No. 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.

Useful 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 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 translate cubic meters V 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, that is, to two decimal places, is sufficient, so the number Pi can be considered equal to 3.14. But since this constant is an irrational number, it has infinite number 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. Calculate the diameter of any pipe correct form is possible using simple calculations, which are based on basic knowledge from school geometry.

You will need

• - measuring tape;
• - 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. Use the measuring scale to 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 a 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 the rectangle, and therefore the diameter of the circle, is equal to square root from 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).

Please 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.

Useful 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, you can download a special program on the Internet.

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're talking about about a circle or circle, you 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

• - measuring ruler;
• - 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 that makes up the outer boundary of the 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, then 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 from each other 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 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 will increase.

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 various levels of complexity.

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 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 only at one point and S equals 0. - If the distance k equals 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.

In the process of carrying out construction work at home or at work, it may become necessary to measure the diameter of a pipe that is already installed in the water supply or sewerage system. It is also necessary to know this parameter at the design stage of laying utility lines.

Hence the need arises to figure out how to determine the diameter of the pipe. The specific measurement method chosen depends on the size of the site and whether the piping location is accessible.

Determining diameter at home

Before measuring the diameter of the pipe, you need to prepare the following tools and devices:

• tape measure or standard ruler;
• calipers;
• camera - it will be used if necessary.

If the pipeline is accessible for measurements, and the ends of the pipes can be measured without problems, then it is enough to have a regular ruler or tape measure at your disposal. It should be borne in mind that this method is used when minimal requirements are imposed on accuracy.

In this case, measure the diameter of the pipes in the following sequence:

1. The prepared tools are applied to the place where the widest part of the end of the product is located.
2. Then count the number of divisions corresponding to the diameter size.

This method allows you to determine the parameters of the pipeline with an accuracy of several millimeters. Sometimes it is necessary to determine the area of ​​the pipeline, which is also very simple to do.

To measure the outer diameter of pipes with a small cross-section, you can use a tool such as a caliper:

1. Spread its legs and apply it to the end of the product.
2. Then they need to be moved so that they are pressed tightly against the outside of the pipe walls.
3. Based on the scale of device values, the required parameter is found out.

This method of determining the pipe diameter gives fairly accurate results, down to tenths of a millimeter.

When the pipeline is not accessible for measurement and is part of an already functioning water supply structure or gas main, proceed as follows: a caliper is applied to the pipe, to its side surface. In this way, the product is measured in cases where the length of the measuring device’s legs exceeds half the diameter of the pipe product.

Often in everyday life there is a need to learn how to measure the diameter of a pipe with a large cross-section. There is a simple way to do this: it is enough to know the circumference of the product and the constant π equal to 3.14. It is not much more difficult to find out the volume of a pipe by performing simple calculations.

First, using a tape measure or a piece of cord, measure the girth of the pipe. Then they substitute the known quantities into the formula d=l:π, where:

d – determined diameter;

l is the length of the measured circle.

For example, the girth of the pipe is 62.8 centimeters, then d = 62.8:3.14 = 20 centimeters or 200 millimeters.

There are situations when the laid pipeline is completely inaccessible. Then you can use the copy method. Its essence lies in the fact that a measuring instrument or a small object whose parameters are known is applied to the pipe.

For example, it could be a box of matches, the length of which is 5 centimeters. Then this section of the pipeline is photographed. Subsequent calculations are performed from the photograph. The photograph measures the apparent thickness of the product in millimeters. Then you need to convert all the obtained values ​​into real pipe parameters, taking into account the scale of the photograph taken.

Measuring diameters in production conditions

At large facilities under construction, pipes are subject to incoming inspection before installation begins. First of all, they check the certificates and markings applied to pipe products.

The documentation must contain certain information regarding the pipes:

• nominal dimensions;
• technical specifications number and date;
• brand of metal or type of plastic;
• product lot number;
• results of the tests performed;
• chem. smelting analysis;
• type of heat treatment;
• X-ray flaw detection results.

In addition, markings containing:

• manufacturer's name;
• heat number;
• product number and its nominal parameters;
• date of manufacture;
• carbon equivalent.

Pipe lengths under production conditions are determined using measuring wire. There are also no difficulties with how to measure the diameter of a pipe with a tape measure.

For first class products, the permissible deviation in one direction or the other from the declared length is 15 millimeters. For second class – 100 millimeters.

The outer diameter of pipes is checked using the formula d = l:π-2Δр-0.2 mm, where in addition to the above values:

Δр – thickness of the tape measure material;

0.2 millimeters is the allowance for the tool to adhere to the surface.

The deviation of the external diameter from that declared by the manufacturer is allowed:

• for products with a cross-section of no more than 200 millimeters–1.5 millimeters;
• for large pipes – 0.7%.

In the latter case, ultrasonic measuring instruments are used to check pipe products. To determine the wall thickness, calipers are used, in which the division on the scale corresponds to 0.01 millimeters. The minus tolerance should not exceed 5% of the nominal thickness. In this case, the curvature cannot be more than 1.5 millimeters per 1 linear meter.

From the information described above, it is clear that it is not difficult to figure out how to determine the diameter of a pipe by its circumference or using simple measuring tools.

A circle is a series of points equidistant from one point, which, in turn, is the center of this circle. The circle also has its own radius, equal to the distance of these points from the center.

The ratio of the length of a circle to its diameter is the same for all circles. This ratio is a number that is mathematical constant, which is denoted by the Greek letter π .

Determining the circumference

You can calculate the circle using the following formula:

L= π D=2 π r

r- circle radius

D- circle diameter

L- circumference

π - 3.14

Task:

Calculate circumference, having a radius of 10 centimeters.

Solution:

Formula for calculating the circumference of a circle has the form:

L= π D=2 π r

where L is the circumference, π is 3.14, r is the radius of the circle, D is the diameter of the circle.

Thus, the length of a circle having a radius of 10 centimeters is:

L = 2 × 3.14 × 5 = 31.4 centimeters

Circle is a geometric figure, which is a collection of all points on the plane remote from given point, which is called its center, to a certain distance not equal to zero and called the radius. Scientists were able to determine its length with varying degrees of accuracy already in ancient times: historians of science believe that the first formula for calculating the circumference was compiled around 1900 BC in ancient Babylon.

With such geometric shapes, like circles, we encounter every day and everywhere. It is its shape that has the outer surface of the wheels that are equipped with various vehicles. This detail, despite its external simplicity and unpretentiousness, is considered one of the greatest inventions of mankind, and it is interesting that the aborigines of Australia and American Indians Until the arrival of Europeans, they had absolutely no idea what it was.

In all likelihood, the very first wheels were pieces of logs that were mounted on an axle. Gradually, the design of the wheel was improved, their design became more and more complex, and their manufacture required the use of a lot of different tools. First, wheels appeared consisting of a wooden rim and spokes, and then, in order to reduce wear on their outer surface, they began to cover it with metal strips. In order to determine the lengths of these elements, it is necessary to use a formula for calculating the circumference (although in practice, most likely, the craftsmen did this “by eye” or simply by encircling the wheel with a strip and cutting off the required section).

It should be noted that wheel is not only used in vehicles. For example, its shape is shaped like a potter's wheel, as well as elements of gears of gears, widely used in technology. Wheels have long been used in the construction of water mills (the oldest structures of this kind known to scientists were built in Mesopotamia), as well as spinning wheels, which were used to make threads from animal wool and plant fibers.

Circles can often be found in construction. Their shape is shaped by fairly widespread round windows, very characteristic of the Romanesque architectural style. The manufacture of these structures is a very difficult task and requires high skill, as well as the availability of special tools. One of the varieties of round windows are portholes installed in ships and aircraft.

Thus, design engineers who develop various machines, mechanisms and units, as well as architects and designers, often have to solve the problem of determining the circumference of a circle. Since the number π , necessary for this, is infinite, it is not possible to determine this parameter with absolute accuracy, and therefore, the calculations take into account the degree of it that in a particular case is necessary and sufficient.