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 a mathematical constant, which is denoted by the Greek letter π .
Determining the circumference of a circle
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 with a radius of 10 centimeters.
Decision:Formula for calculating the dyne of a circle looks like:
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 circumference of a circle with a radius of 10 centimeters is:
L = 2 × 3.14 × 10 = 62.8 centimeters
Circle is a geometric figure, which is a collection of all points on the plane, remote from a given point, which is called its center, at some distance, not equal to zero and called the radius. Scientists knew how 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 of a circle was compiled around 1900 BC in ancient Babylon.
With such geometric figures as circles, we encounter daily and everywhere. It is its shape that has the outer surface of the wheels, which are equipped with various vehicles. This detail, despite its outward simplicity and unpretentiousness, is considered one of the greatest inventions of mankind, and it is interesting that the natives of Australia and the American Indians, until the arrival of the Europeans, 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 improved, their design became more and more complex, and for their manufacture it was necessary to use mass various 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 upholster it with metal strips. In order to determine the lengths of these elements, it is necessary to use the formula for calculating the circumference (although in practice, most likely, the craftsmen did this “by eye” or simply girding the wheel with a strip and cutting off the required section of it).
It should be noted that wheel is used not only in vehicles. For example, a potter's wheel has its shape, as well as elements of gears of gears widely used in technology. Since ancient times, wheels have 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 used to make threads from animal wool and plant fibers.
circles often found in construction. Their shape is quite 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 a special tool. One of the varieties of round windows are portholes installed in ships and aircraft.
Thus, design engineers often have to solve the problem of determining the circumference of a circle, developing various machines, mechanisms and assemblies, as well as architects and designers. Since the number π necessary for this is infinite, then it is not possible to determine this parameter with absolute accuracy, and therefore the calculations take into account that degree of it, which in a particular case is necessary and sufficient.
So the circumference ( C) can be calculated by multiplying the constant π per diameter ( D), or by multiplying π by twice the radius, since the diameter is equal to two radii. Hence, circumference formula will look like this:
C = πD = 2πR
where C- circumference, π - constant, D- circle diameter, R is the radius of the circle.
Since a circle is the boundary of a circle, the circumference of a circle can also be called the length of a circle or the perimeter of a circle.
Problems for the circumference
Task 1. Find the circumference of a circle if its diameter is 5 cm.
Since the circumference is π multiplied by the diameter, then the circumference of a circle with a diameter of 5 cm will be equal to:
C≈ 3.14 5 = 15.7 (cm)
Task 2. Find the circumference of a circle whose radius is 3.5 m.
First, find the diameter of the circle by multiplying the length of the radius by 2:
D= 3.5 2 = 7 (m)
Now find the circumference of the circle by multiplying π per diameter:
C≈ 3.14 7 = 21.98 (m)
Task 3. Find the radius of a circle whose length is 7.85 m.
To find the radius of a circle given its length, divide the circumference by 2. π
Area of a circle
The area of a circle is equal to the product of the number π to the square of the radius. The formula for finding the area of a circle:
S = pr 2
where S is the area of the circle, and r is the radius of the circle.
Since the diameter of a circle is twice the radius, the radius is equal to the diameter divided by 2:
Problems for the area of a circle
Task 1. Find the area of a circle if its radius is 2 cm.
Since the area of a circle is π multiplied by the radius squared, then the area of a circle with a radius of 2 cm will be equal to:
S≈ 3.14 2 2 \u003d 3.14 4 \u003d 12.56 (cm 2)
Task 2. Find the area of a circle if its diameter is 7 cm.
First, find the radius of the circle by dividing its diameter by 2:
7:2=3.5(cm)
Now we calculate the area of the circle using the formula:
S = pr 2 ≈ 3.14 3.5 2 \u003d 3.14 12.25 \u003d 38.465 (cm 2)
This task can be solved in another way. Instead of first finding the radius, you can use the formula for finding the area of a circle in terms of the diameter:
| S = π | D 2 | ≈ 3,14 | 7 2 | = 3,14 | 49 | = | 153,86 | \u003d 38.465 (cm 2) |
| 4 | 4 | 4 | 4 |
Task 3. Find the radius of the circle if its area is 12.56 m 2.
To find the radius of a circle given its area, divide the area of the circle π , and then extract from the result Square root:
r = √S : π
so the radius will be:
r≈ √12.56: 3.14 = √4 = 2 (m)
Number π
The circumference of objects surrounding us can be measured using a centimeter tape or a rope (thread), the length of which can then be measured separately. But in some cases it is difficult or almost impossible to measure the circumference, for example, the inner circumference of a bottle or just the circumference drawn on paper. In such cases, you can calculate the circumference of a circle if you know the length of its diameter or radius.
To understand how this can be done, let's take a few round objects, from which you can measure both the circumference and the diameter. We calculate the ratio of length to diameter, as a result we get the following series of numbers:
From this we can conclude that the ratio of the circumference of a circle to its diameter is a constant value for each individual circle and for all circles as a whole. This relationship is denoted by the letter π .
Using this knowledge, you can use the radius or diameter of a circle to find its length. For example, to calculate the circumference of a circle with a radius of 3 cm, you need to multiply the radius by 2 (so we get the diameter), and multiply the resulting diameter by π . Finally, with the number π we learned that the circumference of a circle with a radius of 3 cm is 18.84 cm.
One line is not enough here, you need to know special formulas. The only thing that is required of us is to determine the diameter or radius of the circle. In some tasks, these quantities are indicated. But what if we have nothing but a drawing? No problem. Diameter and radius can be calculated using a regular ruler. Now let's get down to the most basic.
Formulas everyone should know
As early as almost 4,000 years ago, scientists discovered an amazing relationship: if you divide the circumference of a circle by its diameter, you get the same number, which is approximately 3.14. This meaning was named precisely with this letter in the ancient Greek language, the word "perimeter" and "circumference" began. Based on the discovery made by ancient scientists, you can calculate the length of any circle:
Where P means the length (perimeter) of the circle,
D - diameter, P - "Pi" number.
The circumference of a circle can also be calculated in terms of its radius (r), which is equal to half the length of the diameter. Here is the second formula to remember:
How to find the diameter of a circle?
Represents a chord that passes through the center of the figure. At the same time, it connects the two most distant points in the circle. Based on this, you can independently draw a diameter (radius) and measure its length with a ruler.
Method 1: enter right triangle in a circle
It will not be difficult to calculate the circumference of a circle if we find its diameter. It is necessary to draw in a circle where the hypotenuse will be equal to the diameter of the circle. To do this, you must have a ruler and a square on hand, otherwise nothing will work.
Method 2: enter any triangle
On the side of the circle, mark any three points, connect them - we get a triangle. It is important that the center of the circle lies in the region of the triangle, this can be done by eye. We draw a median to each side of the triangle, the point of their intersection will coincide with the center of the circle. And when we know the center, we can easily draw a diameter using a ruler.
This method is very similar to the first, but can be used in the absence of a square or in cases where it is not possible to draw on a figure, for example, on a plate. It is necessary to take a sheet of paper with right angles. We apply the sheet to the circle so that one vertex of its corner is in contact with the edge of the circle. Next, mark with dots the places where the sides of the paper intersect with the circle line. We connect these points with a pencil and a ruler. If you don't have anything handy, just fold the paper. This line will be equal to the length of the diameter.
Task example
- We are looking for a diameter using a square, a ruler and a pencil according to method No. 1. Suppose it turned out 5 cm.
- Knowing the diameter, we can easily insert it into our formula: P \u003d d P \u003d 5 * 3.14 \u003d 15.7 In our case, it turned out to be about 15.7. Now you can easily explain how to calculate the circumference of a circle without any problems.
The circle calculator is a service specially designed to calculate the geometric dimensions of figures online. Thanks to this service You can easily determine any parameter of a figure based on a circle. For example: You know the volume of a sphere, but you need to get its area. There is nothing easier! Select the appropriate option, enter numerical value and click the calculate button. The service not only displays the results of calculations, but also provides the formulas by which they were made. Using our service, you can easily calculate the radius, diameter, circumference (perimeter of a circle), the area of a circle and a ball, and the volume of a ball.
Calculate Radius
The task of calculating the value of the radius is one of the most common. The reason for this is quite simple, because knowing this parameter, you can easily determine the value of any other parameter of a circle or ball. Our site is built exactly on such a scheme. Regardless of which initial parameter you choose, the radius value is calculated first and all subsequent calculations are based on it. For greater accuracy of calculations, the site uses the number Pi rounded to the 10th decimal place.
Calculate Diameter
Diameter calculation is the simplest type of calculation that our calculator can perform. Getting the diameter value is not difficult at all and manually, for this you do not need to resort to the help of the Internet at all. The diameter is equal to the value of the radius multiplied by 2. The diameter is the most important parameter of the circle, which is extremely often used in Everyday life. Absolutely everyone should be able to calculate it correctly and use it. Using the capabilities of our site, you will calculate the diameter with great accuracy in a fraction of a second.
Find out the circumference of a circle
You can't even imagine how many round objects around us and what an important role they play in our lives. The ability to calculate the circumference is necessary for everyone, from an ordinary driver to a leading design engineer. The formula for calculating the circumference is very simple: D=2Pr. The calculation can be easily carried out both on a piece of paper and with the help of this Internet assistant. The advantage of the latter is that it will illustrate all the calculations with drawings. And to everything else, the second method is much faster.
Calculate the area of a circle
The area of the circle - like all the parameters listed in this article, is the basis of modern civilization. To be able to calculate and know the area of a circle is useful for all segments of the population without exception. It is difficult to imagine an area of science and technology in which it would not be necessary to know the area of a circle. The formula for calculation is again not difficult: S=PR 2 . This formula and our online calculator will help you without extra effort find the area of any circle. Our site guarantees high accuracy of calculations and their lightning-fast execution.
Calculate the area of a sphere
The formula for calculating the area of a sphere is more complicated than formulas described in the previous paragraphs. S=4Pr 2 . This simple set of letters and numbers has been giving people the ability to accurately calculate the area of a sphere for many years. Where can it be applied? Yes, everywhere! For example, you know that the area of the globe is 510,100,000 square kilometers. It is useless to list where knowledge of this formula can be applied. The scope of the formula for calculating the area of a ball is too wide.
Calculate the volume of a sphere
To calculate the volume of the ball, use the formula V=4/3(Pr 3). It was used to create our online service. The site site makes it possible to calculate the volume of a ball in a matter of seconds, if you know any of the following parameters: radius, diameter, circumference, area of a circle or area of a ball. You can also use it for inverse calculations, for example, to know the volume of a ball, get the value of its radius or diameter. Thank you for briefly reviewing the capabilities of our lap calculator. We hope you enjoyed your stay with us and have already added the site to your bookmarks.
Many objects in the world around us are round. These are wheels, round window openings, pipes, various utensils and much more. You can calculate the circumference of a circle by knowing its diameter or radius.
There are several definitions of this geometric figure.
- It is a closed curve consisting of points that are located at the same distance from a given point.
- This is a curve consisting of points A and B, which are the ends of the segment, and all points from which A and B are visible at right angles. In this case, the segment AB is the diameter.
- For the same segment AB, this curve includes all points C such that the ratio AC/BC is constant and does not equal 1.
- This is a curve consisting of points for which the following is true: if you add the squares of the distances from one point to two given other points A and B, you get a constant number greater than 1/2 of the segment connecting A and B. This definition is derived from the Pythagorean theorem.
Note! There are other definitions as well. A circle is an area within a circle. The perimeter of a circle is its length. According to various definitions, a circle may or may not include the curve itself, which is its boundary.
Definition of a circle
Formulas
How to calculate the circumference of a circle using the radius? This is done with a simple formula:
where L is the desired value,
π is the number pi, approximately equal to 3.1413926.
Usually, to find the desired value, it is enough to use π up to the second decimal place, that is, 3.14, this will provide the desired accuracy. On calculators, in particular engineering ones, there may be a button that automatically enters the value of the number π.
Notation
To find through the diameter, there is the following formula:
If L is already known, you can easily find out the radius or diameter. To do this, L must be divided by 2π or π, respectively.
If a circle is already given, you need to understand how to find the circumference from this data. The area of a circle is S = πR2. From here we find the radius: R = √(S/π). Then
L = 2πR = 2π√(S/π) = 2√(Sπ).
Calculating the area in terms of L is also easy: S = πR2 = π(L/(2π))2 = L2/(4π)
Summarizing, we can say that there are three main formulas:
- through the radius – L = 2πR;
- through the diameter - L = πD;
- through the area of a circle – L = 2√(Sπ).
Pi
Without the number π, it will not be possible to solve the problem under consideration. The number π was found for the first time as the ratio of the circumference of a circle to its diameter. This was done by the ancient Babylonians, Egyptians and Indians. They found it quite accurately - their results differed from the now known value of π by no more than 1%. The constant was approximated by such fractions as 25/8, 256/81, 339/108.
Further, the value of this constant was considered not only from the point of view of geometry, but also from the point of view of mathematical analysis through the sums of series. The notation for this constant with the Greek letter π was first used by William Jones in 1706, and became popular after the work of Euler.
It is now known that this constant is an infinite non-periodic decimal, it is irrational, that is, it cannot be represented as a ratio of two integers. With the help of calculations on supercomputers in 2011, they learned the 10-trillion sign of a constant.
It is interesting! To memorize the first few characters of the number π, various mnemonic rules were invented. Some allow you to store big number numbers, for example, one French poem will help you remember pi up to 126 characters.
If you need the circumference, the online calculator will help you with this. There are many such calculators, they only need to enter the radius or diameter. Some of them have both of these options, others calculate the result only through R. Some calculators can calculate the desired value with different accuracy, you need to specify the number of decimal places. Also, using online calculators, you can calculate the area of a circle.
Such calculators are easy to find with any search engine. There are also mobile applications, which will help solve the problem of how to find the circumference of a circle.
Useful video: circumference
Practical use
Solving such a problem is most often necessary for engineers and architects, but in everyday life, knowledge of the necessary formulas can also come in handy. For example, it is required to wrap a cake baked in a form with a diameter of 20 cm with a paper strip. Then it will not be difficult to find the length of this strip:
L \u003d πD \u003d 3.14 * 20 \u003d 62.8 cm.
Another example: you need to build a fence around a circular pool at a certain distance. If the radius of the pool is 10 m, and the fence needs to be placed at a distance of 3 m, then R for the resulting circle will be 13 m. Then its length is:
L \u003d 2πR \u003d 2 * 3.14 * 13 \u003d 81.68 m.
Useful video: circle - radius, diameter, circumference
Outcome
The perimeter of a circle is easy to calculate with simple formulas involving diameter or radius. You can also find the desired value through the area of the circle. Online calculators or mobile applications will help to solve this problem, in which you need to enter a single number - diameter or radius.
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