How to find the area knowing the diameter and length. Circle area: formula

The length of the diameter - a segment passing through the center of the circle and connecting two opposite points of the circle, or the radius - a segment, one of the extreme points of which is located in the center of the circle, and the second - on the arc of the circle. So the diameter equal to length radius multiplied by two.
The value of the number π. This value is a constant - an irrational fraction that has no end. However, it is not periodic. This number expresses the ratio circumference to its radius. To calculate the area of a circle in tasks school course the value of π is used, given to the nearest hundredth - 3.14.

Formulas for finding the area of a circle, its segment or sector

Depending on the specifics of the conditions of the geometric problem, two formulas for finding the area of a circle:

To determine how to find the area of a circle in the easiest way, you need to carefully analyze the conditions of the task.

The school geometry course also includes tasks for calculating the area of segments or sectors for which special formulas are used:

A sector is a part of a circle bounded by a circle and an angle with the vertex located in the center. The area of the sector is calculated by the formula: S = (π*r 2 /360)*А;
- r is the radius;
- A is the angle in degrees.
- r is the radius;
- p is the length of the arc.

There is also a second option S = 0.5 * p * r;

Segment - is a part bounded by a section of a circle (chord) and a circle. Its area can be found by the formula S \u003d (π * r 2 / 360) * A ± S ∆ ;

r is the radius;
A is the angle value in degrees;
S ∆ is the area of a triangle, the sides of which are the radii and the chord of the circle; moreover, one of its vertices is located in the center of the circle, and the other two are located at the points of contact of the arc of the circle with the chord. Important point- the minus sign is placed if the value of A is less than 180 degrees, and the plus sign - if it is more than 180 degrees.

To simplify the solution of a geometric problem, one can calculate circle area online. Special Program quickly and accurately make the calculation in a couple of seconds. How to calculate the area of figures online? To do this, you need to enter the known initial data: radius, diameter, angle.

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). The circumference of a circle is the maximum area of the plane that can be covered with it, 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 a number of 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, a 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.

Sources:

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

The circle calculator is a service specially designed to calculate the geometric dimensions of shapes 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 given 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 find the area of any circle effortlessly. 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 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 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.

In geometry around some set of all points on the plane is called, which 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 theatrical performances were held in circuses and gladiator fights were held, 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 It is no coincidence: the fact is that it is he who provides the minimum necessary geometric parameters of the arena, along which circus horses can run in a circle at a gallop. 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 there is a comprehensive discussion of various important issues and develop ways to solve them. As for the manufacture of the countertops themselves, which have round shape, then specialized tools and equipment are used for their production, subject to the participation of workers with fairly high qualifications.

- this is flat figure, which is a set of points equidistant from the center. All of them are at the same distance and form a circle.

A line segment that connects the center of a circle with points on its circumference is called radius. In each circle, all radii are equal to each other. A line joining two points on a circle and passing through the center is called diameter. The formula for the area of a circle is calculated using a mathematical constant - the number π ..

It is interesting : The number pi. is the ratio of the circumference of a circle to the length of its diameter and is a constant value. The value π = 3.1415926 was used after the work of L. Euler in 1737.

The area of a circle can be calculated using the constant π. and the radius of the circle. The formula for the area of a circle in terms of radius looks like this:

Consider an example of calculating the area of a circle using the radius. Let a circle with radius R = 4 cm be given. Let's find the area of the figure.

The area of our circle will be equal to 50.24 square meters. cm.

There is a formula the area of a circle through the diameter. It is also widely used to calculate the required parameters. These formulas can be used to find .

Consider an example of calculating the area of a circle through the diameter, knowing its radius. Let a circle be given with a radius R = 4 cm. First, let's find the diameter, which, as you know, is twice the radius.

Now we use the data for the example of calculating the area of a circle using the above formula:

As you can see, as a result we get the same answer as in the first calculations.

Knowledge of the standard formulas for calculating the area of a circle will help in the future to easily determine sector area and it is easy to find the missing quantities.

We already know that the formula for the area of a circle is calculated through the product of the constant value π and the square of the radius of the circle. The radius can be expressed in terms of the circumference of a circle and substitute the expression in the formula for the area of a circle in terms of the circumference:
Now we substitute this equality into the formula for calculating the area of a circle and get the formula for finding the area of \u200b\u200bthe circle, through the circumference

Consider an example of calculating the area of a circle through the circumference. Let a circle be given with length l = 8 cm. Let's substitute the value in the derived formula:

The total area of the circle will be 5 square meters. cm.

Area of a circle circumscribed around a square

It is very easy to find the area of a circle circumscribed around a square.

This will require only the side of the square and knowledge of simple formulas. The diagonal of the square will be equal to the diagonal of the circumscribed circle. Knowing the side a, it can be found using the Pythagorean theorem: from here.
After we find the diagonal, we can calculate the radius: .
And then we substitute everything into the basic formula for the area of a circle circumscribed around a square: