How to calculate the area of a circle given the diameter. Circle area: formula. What is the area of a circle circumscribed and inscribed in a square, a right-angled and isosceles triangle, a right-angled, isosceles trapezoid

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 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), 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 precision calculations and their lightning-fast execution.

Calculate the area of a sphere

The formula for calculating the area of a ball is no more complicated than the 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 the 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 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 seconds, if you know any of the following parameters: radius, diameter, circumference, area of a circle, or area of a sphere. 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.

As we know from the school curriculum, it is customary to call a circle a flat geometric figure, which consists of many points equidistant from the center of the figure. Since they are all at the same distance, they form a circle.

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Circle Area Calculator

The line segment connecting the center of the circle and the points on its circumference is called the radius. In this case, in each circle, all radii are equal to each other. The diameter of a circle is a straight line that connects two points on a circle and passes through its center. We need all this for correct calculation circle area. In addition, this value is calculated using the Pi number.

How to calculate the area of a circle

For example, we have a circle with a radius of four centimeters. Let's calculate its area: S=(3.14)*4^2=(3.14)*16=50.24. Thus, the area of the circle is 50.24 square centimeters.

Also, there is a special formula for calculating the area of a circle through the diameter: S=(pi/4) d^2.

Let's look at an example of such a calculation of a circle through its diameter, knowing the radius of the figure. For example, we have a circle with a radius of four centimeters. First you need to find the diameter, which is twice the radius itself: d=2R, d=2*4=8.

Now you should use the data obtained to calculate the area of the circle using the above formula: S=((3.14)/4)*8^2=0.785*64=50.24.

As you can see, in the end we get the same answer as in the first case.

Knowledge of the above standard formulas for the correct calculation of the area of the circle will help you easily find the missing values and determine the area of the sectors.

So, we know that the formula for calculating the area of a circle is calculated by multiplying the constant value of Pi by the square of the radius of the circle itself. The radius itself can be expressed in terms of the actual circumference by substituting the expression in terms of the circumference into the formula. That is: R=l/2pi.

Now we need to substitute this equation into the formula for calculating the area of a circle, and as a result we get the formula for finding the area of this geometric figure through the circumference: S=pi((l/2pi))^2=l^2/(4pi).

For example, we are given a circle whose circumference is eight centimeters. We substitute the value in the considered formula: S=(8^2)/(4*3.14)=64/(12.56)=5. And we get the area of the circle equal to five square centimeters.

In geometry around is called a set of all points on the plane that are removed from one point, called its center, at a distance not greater than a given one, called its radius. In this case, the outer boundary of the circle is circle, and if the length of the radius is equal to zero, a circle degenerates to a point.

Determining the area of a circle

If necessary area of a circle can be calculated using the formula:

pr 2

r- circle radius

D- circle diameter

S- area of a circle

π - 3.14

This geometric figure very common in both engineering and architecture. Designers of machines and mechanisms develop various parts, the sections of many of which are precisely a circle. For example, these are shafts, rods, rods, cylinders, axles, pistons, and so on. In the manufacture of these parts, blanks are used various materials(metals, wood, plastics), their sections also represent precisely a circle. It goes without saying that developers often have to calculate area of a circle through a diameter or radius, using simple mathematical formulas discovered in ancient times.

Exactly then round elements began to be actively and widely used in architecture. One of the most striking examples of this is the circus, which is a kind of buildings designed to host various entertainment events. Their arenas are shaped circle, and for the first time they began to be built in antiquity. The very word " circle» translated from Latin means " a circle". If in ancient times circuses hosted theatrical performances and gladiator fights, now they serve as a place where circus performances are almost exclusively held with the participation of animal trainers, acrobats, magicians, clowns, etc. The standard diameter of the circus arena is 13 meters, and this is completely not by chance: the fact is that it is he who provides the minimum necessary geometric parameters an arena where circus horses can gallop in circles. If we calculate area of a circle through the diameter, it turns out that for the circus arena this value is 113.04 square meters.

The architectural elements that can take the form of a circle are windows. Of course, in most cases they are rectangular or square (largely due to the fact that it is easier for both architects and builders), but in some buildings you can also find round windows. Moreover, in such vehicles, like air, sea and river vessels, they are most often just that.

It is by no means uncommon to use round elements for the production of furniture such as tables and chairs. There is even a concept round table ”, which implies a constructive discussion, during which a comprehensive discussion of various important problems takes place and ways to solve them are developed. As for the manufacture of the countertops themselves, which have a round shape, they are used for their production specialized tools and equipment, subject to the participation of fairly highly skilled workers.

Instruction

Use pi to find the radius famous area circle. This constant specifies the proportion between the diameter of a circle and the length of its border (circle). Circumference maximum area plane, which it is possible to cover with its help, and the diameter is equal to two radii, therefore, the area with the radius also correlate with each other with a proportion that can be expressed in terms of Pi. This constant (π) is defined as the area (S) and the squared radius (r) of the circle. It follows from this that the radius can be expressed as Square root from the quotient of dividing the area by Pi: r=√(S/π).

For a long time, Erastofen headed the Library of Alexandria, the most famous library ancient world. In addition to the fact that he calculated the size of our planet, he made another series important inventions and discoveries. Invented a simple method to determine prime numbers, now called "Erastothenes' sieve".

He drew a "map of the world", in which he showed all parts of the world known at that time to the ancient Greeks. The map was considered one of the best for its time. Developed a system of longitude and latitude and a calendar that included leap years. Invented the armillary sphere mechanical device used by early astronomers to demonstrate and predict the apparent movement of stars in the sky. He also compiled a star catalog, which included 675 stars.

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The Greek scientist Eratosthenes of Cyrene for the first time in the world calculated the radius of the Earth
Eratosthenes "Calculation of Earth" s Circumference
Eratosthenes