To write how to find the diameter of a circle, you must first define what it is. So, the diameter of a circle is a straight line that passes through the center of the circle and connects points on the circle.

Below we will look at ways to find the diameter of a circle through its length, the area of ​​the inscribed circle, and through the radius.

Diameter determination

It is generally accepted that no matter the size of a circle, the ratio of its length to its diameter is a constant number “Pi”, which is approximately equal to 3.14. To understand how to find the diameter of a circle, you should give formulas and use an example to show the calculations of this value.

Radius

If the radius of the circle is known, then the diameter is very easy to calculate:

D = 2R, where D is the diameter and R is the radius. It turns out that the diameter is equal to two radii. For example, it is known that the radius is 10 cm, then we calculate the diameter as follows: D = 2*10, it turns out that the diameter is 20 cm.

Circumference

In case the circumference of the circle is known, the number can be useful for calculation. Here's the formula you can use: D = l/, where l is the length of the circle. It turns out that if the circumference is 18 cm, then the diameter is calculated as follows: D = 18 / 3.14 ≈ 5.73 cm.

Area of ​​a circle

If only the area of ​​the circle is known, then this value can also be applied. In this case, the area is denoted by the letter S. Based on the formula S = R 2, you can find the radius, and therefore the diameter. So, radius R = √ (S / ). To find the radius, divide the area by Pi and extract from this value Square root. Thus, if the area is 25 cm, then the radius is calculated as follows: R = √ (25 / 3.14) ≈ √8 ≈ 2.8 cm. Then the diameter can be calculated: D = 2R, D = 2.8*2= 5.6 cm.

You can read more about finding the diameter in the article.

Instructions

Diameter is a line segment connecting two arbitrary points on circle and passing through its center. Therefore, if diameter need to be found, knowing the radius of a given circle, then you should multiply the numerical value of the radius by two, and measure the found value in the same units as the radius. Example: Radius circle 4 centimeters. Find diameter this circle. Solution: The diameter is 4 cm*2=8 cm. Answer: 8 centimeters.

If the diameter needs to be found through the length circle, then you need to act using step one. There is a formula to calculate the length circle: l=2пR, where l is the length circle, 2 is a constant, n is a number equal to 3.14; R - radius circle. Knowing that diameter- this is double the radius, the above formula can be written as: l=пD, where D - diameter.

Express from this formula diameter circle: D=l/p. And substitute all known quantities into it, calculating linear equation with one unknown. Example: Find diameter circle, if its length is 3 meters. Solution: diameter equals 3/3 = 1m. Answer: diameter equal to one meter.

Circle represents a figure of a plane whose points are equally distant from its center, and diameter circle - a segment passing through this center and connecting the two most distant points of the circle. Exactly diameter often becomes the quantity that allows us to solve most problems in geometry in finding a circle.

Instructions

For example, to find the circumference, it is enough to define the known diameter. Ask what you know diameter circle equal to N, and draw a circle in accordance with these data. Because the diameter connects two points of the circle and passes through the center, therefore, the radius of the circle will always be equal to half the value diameter a, that is, r = N/2.

Use the mathematical constant π to find the length or any other quantity. It represents the ratio of the circumference value to the length value diameter and the circle in geometric calculations is taken to be equal to π ≈ 3.14.

To determine the circumference, take the standard formula L = π*D and substitute the value diameter and D = N. As a result diameter, multiplied by 3.14, will show the approximate circumference.

In the case when you need to determine not only the circumference, but also its area, also use the value of the constant π. Only this time, use a different formula, according to which the area of ​​a circle is defined as the length of the radius squared and multiplied by the number π. Accordingly, the formula looks like this: S = π*(r^2).

Since the initial data determines that the radius is r = N/2, therefore, the formula for the area of ​​a circle is modified: S = π*(r^2) = π*((N/2)^2). As a result, if you substitute the value of a known diameter ah, you will get the required area.

Don't forget to check in what units of measurement you need to determine the length or area of ​​a circle. If the source data determines that diameter is measured in millimeters, the area of ​​a circle must also be measured in millimeters. For other units - cm2 or m2, calculations are made similarly.

Circumference and diameter are interrelated geometric quantities. This means that the first of them can be translated into the second without any additional data. The mathematical constant through which they are related to each other is the number π.

Instructions

If the circle is represented as an image on paper and its diameter needs to be determined approximately, measure it directly. If its center is shown in the drawing, draw a line through it. If the center is not shown, find it using a compass. To do this, use a square with angles of 90 and 45 degrees. Attach it at a 90-degree angle to the circle so that both legs touch it, and trace it. Then applying the 45-degree angle of the square to the resulting right angle, draw a bisector. It will pass through the center of the circle. Then, in the same way, draw a second right angle and its bisector in another place on the circle. They will intersect in the center. This will allow you to measure the diameter.

The diameter of a circle is the straight line segment that connects the two points of the circle that are most distant from each other, passing through the center of the circle. The name diameter comes from Greek language and literally translated it meant transverse. The diameter is indicated by the letter D of the Latin alphabet or the symbol O.

Circle diameter

In order to know how to find the diameter of a circle, you need to refer to the formulas. There are two basic formulas by which you can calculate the diameter of a circle. The first is D = 2R. Here the diameter is equal to twice the radius, where the radius is the distance from the center to any point on the circle (R). Let's consider an example: if the radius is known in the task and it is equal to 10 cm, then you can easily find the diameter. For this radius value, we substitute D = 2 * 10 = 20 cm into the formula

The second formula makes it possible to find the diameter along the circumference and it looks like this: D = L/P, where L is the value of the circumference, and P is the number Pi, which is approximately equal to 3.14. This formula is very convenient to use in practice. If you need to know the diameter of a hatch, tank cover, or some kind of pit, you just need to measure their circumference and divide it by 3.14. For example, the circumference is 600 cm, hence D = 600/3.14 = 191.08 cm.

Circumcircle diameter

The diameter of a circumscribed circle can also be found if it is circumscribed or inscribed in a triangle. To do this, you first need to find the radius for the inscribed circle using the formula: R = S/p, where S denotes the area of ​​the triangle, and p is its semi-perimeter, p is equal to (a + b + c)/2. Once the radius is known, you need to use the first formula. Or immediately substitute all values ​​into the formula D = 2S/p.

If you don't know how to find the diameter of a circumscribed circle, use the formula to find the radius of a circle circumscribed by a triangle. R = (a * b * c)/4 * S, S in the formula denotes the area of ​​the triangle. Then, in the same way, substitute the value of the radius into the formula D = 2R.

Instructions

Diameter (from the ancient Greek διάμετρος “diameter, diameter”) is a segment that connects two points on a circle or sphere, passing through the center of this circle or sphere. The diameter is also called the length of this segment. Radius (from the Latin radius “ray, spoke of a wheel”) is a segment that connects the center of a circle or sphere with any point located on this circle or sphere; the radius is also the length of this segment.

The radius is usually denoted by the letter r, the diameter by the letter d. By definition, the radius is equal to half the diameter, and the diameter is equal in magnitude to two radii. Accordingly, d=2r, r=d/2. This means that in order to find out the radius, knowing the diameter, you need to divide the diameter by two.

Example. The diameter of the circle d is 8. What is the radius r? Solution: r=d/2, which means that to find the radius, you need to divide the diameter value 8 by two. 8/2=4. Answer: r=4, radius is four.

If you are looking for the length of a radius or diameter, remember that the length cannot be a negative number. Therefore, if during the solution you came to the formula d=2r= √x (square root of x), and x is equal to, for example, 16, then the diameter d=±4, and the radius r=±2. Since the length cannot be a negative number, you get the answer: the diameter is four, the radius is two.

An interesting fact is that the word “radius” is also found in anatomy; it refers to one of the bones of the forearm, the radius (located outward and slightly anterior to the ulna). And the word radius has a meaning that goes back to ancient Rome - it is the name of a short Roman sword that was used by legionnaires for defense. The legionnaire said: “Here I am and Rome!” – he drew a line on the ground with this sword and defended himself to the last.

Definition radius circle is one of the main tasks of mathematics. There are many formulas for accounting radius, you just need to know some standard parameters. Graphically, the radius is indicated using the letter R of the Latin alphabet.

Instructions

A circle is a closed curve. The points located in its plane are equidistant from the center, which lies in the same plane as the curve. Radius - segment circle, connecting its center with any of its points. With its help, you can find out many other parameters of the figure, so it is a key parameter. Numerical value radius will be the length of this segment.

You should also distinguish the radius of a figure from its diameter (the diameter connects the two points that are furthest apart from each other). To use the mathematical method of finding radius need to know the length or diameter circle. In the first case, the formula will look like “R = L/2?”, where L is the known length circle, and the number? equals 3.14 and is used to denote a specific irrational number.

If only the diameter is known, the formula will look like “R = D/2”.

If length circle is unknown, but there is data on the length and height of a certain segment, then the formula will look like “R = (h^2*4 + L^2)/8*h”, where h is the height of the segment (is the distance from the middle of the chord to the very the protruding part of the specified arc), and L is the length of the segment (which is not the length of the chord). A chord is a line segment that connects two points circle.

note

It is necessary to distinguish between the concepts of “circle” and “circle”. A circle is part of a plane, which, in turn, is limited by a circle of a certain radius. To find the radius, you need to know the area of ​​the circle. In this case, the equation will be “R = (S/π)^1/2”, where S is the area. To calculate the area, in turn, you need to know the radius (“S = πr^2”).

Knowing only the length diameter circles, you can calculate not only square circle, but also the area of ​​some others geometric shapes. This follows from the fact that the diameters of circles inscribed or circumscribed around such figures coincide with the lengths of their sides or diagonals.

Instructions

If you need to find square circle (S) along its known length diameter(D), multiply pi (π) by the squared length diameter, and divide the result by four: S=π ²*D²/4. For example, if the diameter of a circle is twenty centimeters, then its square can be calculated as follows: 3.14² * 20² / 4 = 9.86 * 400 / 4 = 986 square centimeters.

If you need to find square square (S) along the diameter of the circle (D) described around it, construct the length diameter squared, and divide the result in half: S=D²/2. For example, if the diameter of the circumscribed circle is twenty centimeters, then square square can be calculated as follows: 20² / 2 = 400 / 2 = 200 square centimeters.

If square square (S) must be found by the diameter of the circle inscribed in it (D), it is enough to construct the length diameter squared: S=D². For example, if the diameter of the inscribed circle is twenty centimeters, then square square can be calculated as follows: 20² = 400 square centimeters.

If you need to find square right triangle (S) according to known diameter m inscribed (d) and circumscribed (D) circles around it, then construct the length diameter inscribed circle into a square and divide by four, and to the result add half the product of the lengths of the diameters of the inscribed and circumscribed circles: S=d²/4 + D*d/2. For example, if the diameter of the circumscribed circle is twenty centimeters, and the inscribed circle is ten centimeters, then square triangle can be calculated as follows: 10² / 4 + 20 * 10/2 = 25 + 100 = 125 square centimeters.

Use the built-in Google search calculator to make the necessary calculations. For example, to calculate using this search engine square a right triangle according to the example from the fourth step, you need to enter the following search query: “10^2 / 4 + 20*10/2”, and then press the Enter key.

Instructions

To find the diameter, use one of the main properties of a circle, which is that the ratio of the length of its perimeter to the diameter is the same for absolutely all circles. Of course, such constancy did not go unnoticed by mathematicians, and this proportion has long received its own name - this is the number Pi (π is the first letter Greek words « circle" and "perimeter"). The numerical expression of this constant is determined by the length of a circle whose diameter is equal to one.

Divide the known circumference of a circle by Pi to calculate its diameter. Since this number is “irrational”, it has no finite value - it is an infinite fraction. Round Pi according to the accuracy of the result you need to obtain.

Use some kind of calculator to calculate the length of the diameter if you can’t do it in your head. For example, you can use the one that is built into the Nigma or Google search engine - it understands mathematical operations, entered in “human” language. For example, if the known circumference is four meters, then to find the diameter you can “humanly” ask the search engine: “4 meters divided by pi.” But if you enter, for example, “4/pi” into the search query field, then the search engine will understand this formulation of the problem. In any case, the answer will be “1.27323954 meters”.

Use the Windows calculator software if you are more familiar with interfaces with regular buttons. In order not to look for a link to launch it in the deep levels of the system’s main menu, press the WIN + R key combination, enter the calc command and press the Enter key. The interface of this program differs very slightly from conventional calculators, so the operation of dividing the circumference by Pi is unlikely to cause any difficulties.

Official diameter of the Earth

The diameter of the Earth is determined by where it will be measured. For convenience, two indicators are taken as the officially recognized diameter: the diameter of the Earth at the equator and the distance between the North and South Poles. The first indicator is 12,756.274 km, and the second is 12,714, the difference between them is slightly less than 43 km.

These numbers do not make much of an impression; they are even inferior to the distance between Moscow and Krasnodar - two cities located in the same country. However, it was not easy to figure them out.

Calculating the diameter of the Earth

The diameter of the planet is calculated using the same geometric formula as any other diameter.

To find the perimeter of a circle, you need to multiply its diameter by the number pi. Consequently, to find the diameter of the Earth, you need to measure its circumference in the appropriate section (along the equator or in the plane of the poles) and divide it by the number pi.

The first person to try to measure the circumference of the Earth was the ancient Greek scientist Eratosthenes of Cyrene. He noticed that in Siena (now Aswan) on the day of the summer solstice, the Sun was at its zenith, illuminating the bottom of a deep well. In Alexandria on that day it was 1/50 of the circle away from the zenith. From this, the scientist concluded that the distance from Alexandria to Syene is 1/50 of the circumference of the Earth. The distance between these cities is 5,000 Greek stadia (approximately 787.5 km), therefore the circumference of the Earth is 250,000 stadia (approximately 39,375 km).

Modern scientists have more advanced means of measurement at their disposal, but their theoretical basis corresponds to the idea of ​​Eratosthenes. At two points located several hundred kilometers from each other, the position of the Sun or certain stars in the sky is recorded and the difference between the results of the two measurements is calculated in degrees. Knowing the distance in kilometers, it is easy to calculate the length of one degree and then multiply it by 360.

To clarify the size of the Earth, both laser ranging and satellite observation systems are used.

Today it is believed that the circumference of the Earth at the equator is 40,075.017 km, and at the meridian - 40,007.86. Eratosthenes was only slightly mistaken.

The size of both the circumference and diameter of the Earth is increasing due to meteorite matter that constantly falls on the Earth, but this process is very slow.

Sources:

• How the Earth was measured

Video on the topic

Sources:

• radius on formula.ru website

Word " geometry " comes from the merger of Greek words " Earth" And " I'm measuring" While measurements of our home planet hardly threaten us, smaller-scale calculations haunt us almost constantly. For example, many unexpectedly had to deal with the issue of measuring the diameter of a circle, and for this there are several simple ways, which do not require special skills. How to find the diameter of a circle, and what is the use Everyday life this may bring, we will try to figure it out.

Instructions:

• To begin with, let’s remember what “ diameter " This is a segment connecting the two most distant points on it and passing through its center (usually denoted - D or Ø ).
• Given a known radius , which is the distance from the center to any point on the circle ( R), the diameter can be calculated using the formula: D=2R. That is, it is enough to double the radius value. Let's say the radius is 7 cm, then the diameter is: 7*2 = 14 cm.
• Now consider a more complex situation in which we need to find the diameter of a circle, knowing only its length. In such a case, you need to divide the length by the number Pi. Pi is a designation for an irrational number used in mathematics, approximately equal to 3,14 . For example, the length is 25 cm, then the required value is: 25 / 3.14 = 7.96 cm.
• You can also find out the diameter of a circle thanks to the area of ​​the circle bounded by it. It looks like this: 2 * √(S/Pi) = D, Where S– area value. To find out the actual area of ​​a circle, you need to know