Calculation of a circle by diameter. How to find and what will be the circumference of a circle?
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A circle is a curved line that encloses a circle. In geometry, shapes are flat, so the definition refers to a two-dimensional image. It is assumed that all points of this curve are located at an equal distance from the center of the circle.
The circle has several characteristics on the basis of which calculations related to this geometric figure are made. These include: diameter, radius, area and circumference. These characteristics are interrelated, that is, to calculate them, information about at least one of the components is sufficient. For example, knowing only the radius of a geometric figure, you can use the formula to find the circumference, diameter, and area.
- The radius of a circle is the segment inside the circle connected to its center.
- A diameter is a segment inside a circle connecting its points and passing through the center. Essentially, the diameter is two radii. This is exactly what the formula for calculating it looks like: D=2r.
- There is one more component of a circle - a chord. This is a straight line that connects two points on a circle, but does not always pass through the center. So the chord that passes through it is also called the diameter.
How to find out the circumference? Let's find out now.
Circumference: formula
The Latin letter p was chosen to denote this characteristic. Archimedes also proved that the ratio of the circumference of a circle to its diameter is the same number for all circles: this is the number π, which is approximately equal to 3.14159. The formula for calculating π is: π = p/d. According to this formula, the value of p is equal to πd, that is, the circumference: p= πd. Since d (diameter) is equal to two radii, the same formula for the circumference can be written as p=2πr. Let's consider the application of the formula using simple problems as an example:
Problem 1
At the base of the Tsar Bell the diameter is 6.6 meters. What is the circumference of the base of the bell?
- So, the formula for calculating the circle is p= πd
- Substitute the existing value into the formula: p=3.14*6.6= 20.724
Answer: The circumference of the bell base is 20.7 meters.
Problem 2
The artificial satellite of the Earth rotates at a distance of 320 km from the planet. The radius of the Earth is 6370 km. What is the length of the satellite's circular orbit?
- 1. Calculate the radius of the circular orbit of the Earth satellite: 6370+320=6690 (km)
- 2.Calculate the length of the satellite’s circular orbit using the formula: P=2πr
- 3.P=2*3.14*6690=42013.2
Answer: the length of the circular orbit of the Earth satellite is 42013.2 km.
Methods for measuring circumference
Calculating the circumference of a circle is not often used in practice. The reason for this is the approximate value of the number π. In everyday life, to find the length of a circle, they use special device– curvimeter. An arbitrary starting point is marked on the circle and the device is led from it strictly along the line until they reach this point again.
How to find the circumference? You just need to keep simple calculation formulas in your head.
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 and 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 × 10 = 62.8 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.
We encounter geometric shapes such as circles 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 greatest inventions humanity, and it is interesting that the aborigines of Australia and American Indians, until the arrival of 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 was improved, their design became more and more complex, and for their manufacture it was necessary to use a lot of various instruments. First, wheels appeared consisting of a wooden rim and spokes, and then, in order to reduce their wear 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, it 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 special tool. 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, then with absolute precision it is not possible to determine this parameter, and therefore the calculations take into account its degree, which in one or another specific case is necessary and sufficient.
The circle occurs at Everyday life no less often than a rectangle. And for many people, the problem of how to calculate the circumference is difficult. And all because it has no corners. If they were available, everything would become much simpler.
What is a circle and where does it occur?
This flat figure represents a number of points that are located at the same distance from another one, which is the center. This distance is called the radius.
In everyday life, it is not often necessary to calculate the circumference of a circle, except for people who are engineers and designers. They create designs for mechanisms that use, for example, gears, portholes and wheels. Architects create houses that have round or arched windows.
Each of these and other cases requires its own precision. Moreover, it turns out to be impossible to calculate the circumference absolutely accurately. This is due to the infinity of the main number in the formula. "Pi" is still being refined. And the rounded value is most often used. The degree of accuracy is chosen to give the most correct answer.
Designations of quantities and formulas
Now it’s easy to answer the question of how to calculate the circumference of a circle by radius; for this you will need the following formula:
Since radius and diameter are related to each other, there is another formula for calculations. Since the radius is two times smaller, the expression will change slightly. And the formula for how to calculate the circumference of a circle, knowing the diameter, will be as follows:
l = π * d.
What if you need to calculate the perimeter of a circle?
Just remember that a circle includes all the points inside the circle. This means that its perimeter coincides with its length. And after calculating the circumference, put an equal sign with the perimeter of the circle.
By the way, their designations are the same. This applies to radius and diameter, and the perimeter is the Latin letter P.
Examples of tasks
Task one
Condition. Find out the length of a circle whose radius is 5 cm.
Solution. Here it is not difficult to understand how to calculate the circumference. You just need to use the first formula. Since the radius is known, all you need to do is substitute the values and calculate. 2 multiplied by a radius of 5 cm gives 10. All that remains is to multiply it by the value of π. 3.14 * 10 = 31.4 (cm).
Answer: l = 31.4 cm.
Task two
Condition. There is a wheel whose circumference is known and equal to 1256 mm. It is necessary to calculate its radius.
Solution. In this task you will need to use the same formula. But only the known length will need to be divided by the product of 2 and π. It turns out that the product will give the result: 6.28. After division, the number left is: 200. This is the desired value.
Answer: r = 200 mm.
Task three
Condition. Calculate the diameter if the circumference of the circle is known, which is 56.52 cm.
Solution. Similar to the previous problem, you will need to divide the known length by the value of π, rounded to the nearest hundredth. As a result of this action, the number 18 is obtained. The result is obtained.
Answer: d = 18 cm.
Problem four
Condition. The clock hands are 3 and 5 cm long. You need to calculate the lengths of the circles that describe their ends.
Solution. Since the arrows coincide with the radii of the circles, the first formula is required. You need to use it twice.
For the first length, the product will consist of factors: 2; 3.14 and 3. The result will be 18.84 cm.
For the second answer, you need to multiply 2, π and 5. The product will give the number: 31.4 cm.
Answer: l 1 = 18.84 cm, l 2 = 31.4 cm.
Task five
Condition. A squirrel runs in a wheel with a diameter of 2 m. How far does it run in one full revolution of the wheel?
Solution. This distance is equal to the circumference. Therefore, you need to use a suitable formula. Namely, multiply the value of π and 2 m. Calculations give the result: 6.28 m.
Answer: The squirrel runs 6.28 m.
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 lie within the boundaries of the circle. Therefore, the length of the figure is equal to the perimeter of the circle.
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. Interior 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. The rule applies to each point that makes up the figure: the sum of the squares of the 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 the 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 in everyday life you may encounter this need, for example, when building a fence around a pool round shape. 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 are located 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. According to these parameters there is required size circle: 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:
- At small sizes of a round object, 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 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.
Circle calculator is a service specially designed to calculate geometric dimensions 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 ball, but you need to get its area. Nothing could be easier! Select the appropriate option, enter a numeric 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), area of a circle and ball, and volume of a ball.
Calculate radius
The task of calculating the radius value 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 this scheme. Regardless of what initial parameter you have chosen, the radius value is first calculated and all subsequent calculations are based on it. For greater accuracy of calculations, the site uses Pi, rounded to the 10th decimal place.
Calculate diameter
Calculating diameter is the simplest type of calculation that our calculator can perform. It is not at all difficult to obtain the diameter value manually; for this you do not need to resort to the Internet at all. Diameter is equal to the radius value multiplied by 2. Diameter – the most important parameter circle, which is extremely often used in everyday life. Absolutely everyone should be able to calculate and use it correctly. Using the capabilities of our website, you will calculate the diameter with great accuracy in a fraction of a second.
Find out the circumference
You can’t even imagine how many round objects there are 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 done either on a piece of paper or using this internet assistant The advantage of the latter is that it illustrates all calculations with pictures. And on top of 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 modern civilization. Being 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 a field 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 out the area of any circle. Our site guarantees high accuracy calculations and their lightning-fast execution.
Calculate the area of a sphere
The formula for calculating the area of a ball is not at all more complex formulas described in the previous paragraphs. S=4Pr 2 . This simple set of letters and numbers has been giving people the ability to fairly accurately calculate the area of a ball for many years. Where can this be applied? Yes everywhere! For example, you know that the area globe equal to 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 sphere is too wide.
Calculate the volume of the ball
To calculate the volume of the ball, use the formula V = 4/3 (Pr 3). It was used to create our online service. The website 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 reverse calculations, for example, to know the volume of a ball to obtain the value of its radius or diameter. Thank you for taking a quick look at the capabilities of our circle calculator. We hope you liked our site and have already bookmarked the site.