home
Psychology of fear
The area of the circle is 32 mm. Circle area: formula

The area of the circle is 32 mm. Circle area: formula

21.10.2019

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 is very common both in engineering and in 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 from various materials (metals, wood, plastics) are used, their sections also represent precisely a circle. It goes without saying that developers often have to calculate area of a circle through the diameter or radius, using for this purpose 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" in 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 as air, sea and river vessels, they are most often just like 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 tabletops themselves, which have a round shape, specialized tools and equipment are used for their production, subject to the participation of workers with fairly high qualifications.

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.

Convenient article navigation:

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 to correctly calculate the area of the circle. 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.

Knowing the standard formulas described above for the correct calculation of the area of a 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.

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 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 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.

A circle is a visible collection of many points that are at the same distance from the center. To find its area, you need to know what the radius, diameter, π number and circumference are.

Quantities involved in calculating the area of a circle

The distance bounded by the central point of the circle and any of the points of the circle is called the radius of this geometric figure. The lengths of all radii of one circle are the same. The line segment between any 2 points on the circle that passes through the center point is called the diameter. The length of the diameter is equal to the length of the radius multiplied by 2.

To calculate the area of a circle, the value of the number π is used. This value is equal to the ratio of the circumference to the length of the diameter of the circle and has a constant value. Π = 3.1415926. The circumference is calculated using the formula L=2πR.

Find the area of a circle using the radius

Therefore, the area of a circle is equal to the product of the number π and the radius of the circle raised to the 2nd power. As an example, let's take the length of the radius of the circle equal to 5 cm. Then the area of the circle S will be equal to 3.14 * 5 ^ 2 = 78.5 square meters. cm.

Circle area in terms of diameter

The area of a circle can also be calculated by knowing the diameter of the circle. In this case, S = (π/4)*d^2, where d is the diameter of the circle. Let's take the same example where the radius is 5 cm. Then its diameter will be 5*2=10 cm. The area of the circle is S=3.14/4*10^2=78.5 sq.cm. The result, which is equal to the total of the calculations in the first example, confirms the correctness of the calculations in both cases.

Area of a circle in terms of circumference

If the radius of a circle is represented through the circumference, then the formula will look like this: R=(L/2)π. Substitute this expression into the formula for the area of a circle and as a result we get S=(L^2)/4π. Consider an example in which the circumference is 10 cm. Then the area of the circle is S = (10 ^ 2) / 4 * 3.14 = 7.96 square meters. cm.

Area of a circle in terms of the length of a side of an inscribed square

If a square is inscribed in a circle, then the length of the diameter of the circle is equal to the length of the diagonal of the square. Knowing the size of the side of the square, you can easily find the diameter of the circle by the formula: d ^ 2 \u003d 2a ^ 2. In other words, the diameter to the power of 2 is equal to the side of the square to the power of 2 times 2.

Having calculated the value of the length of the diameter of a circle, you can also find out its radius, and then use one of the formulas for determining the area of a circle.

Sector area of a circle

A sector is a part of a circle bounded by 2 radii and an arc between them. To find out its area, you need to measure the angle of the sector. After that, it is necessary to compose a fraction, in the numerator of which there will be the value of the angle of the sector, and in the denominator - 360. To calculate the area of \u200b\u200bthe sector, the value obtained as a result of dividing the fraction must be multiplied by the area of \u200b\u200bthe circle calculated using one of the above formulas.

Circles require a more careful approach and are much less common in B5 tasks. At the same time, the general solution scheme is even simpler than in the case of polygons (see the lesson “Polygon areas on a coordinate grid”).

All that is required in such tasks is to find the radius of the circle R . Then you can calculate the area of the circle using the formula S = πR 2 . It also follows from this formula that it suffices to find R 2 for the solution.

To find the indicated values, it is enough to indicate on the circle a point lying at the intersection of the grid lines. And then use the Pythagorean theorem. Consider specific examples of calculating the radius:

A task. Find the radii of the three circles shown in the figure:

Let's perform additional constructions in each circle:

In each case point B is chosen on the circle to lie at the intersection of the grid lines. Point C in circles 1 and 3 completes the figure to a right triangle. It remains to find the radii:

Consider triangle ABC in the first circle. According to the Pythagorean theorem: R 2 \u003d AB 2 \u003d AC 2 + BC 2 \u003d 2 2 + 2 2 \u003d 8.

For the second circle, everything is obvious: R = AB = 2.

The third case is similar to the first. From the triangle ABC according to the Pythagorean theorem: R 2 \u003d AB 2 \u003d AC 2 + BC 2 \u003d 1 2 + 2 2 \u003d 5.

Now we know how to find the radius of a circle (or at least its square). Therefore, we can find the area. There are tasks where it is required to find the area of a sector, and not the entire circle. In such cases, it is easy to find out what part of the circle is this sector, and thus find the area.

A task. Find the area S of the shaded sector. Indicate S / π in your answer.

Obviously, the sector is one quarter of the circle. Therefore, S = 0.25 S of the circle.

It remains to find the S of the circle - the area of the circle. To do this, we will perform an additional construction:

Triangle ABC is a right triangle. By the Pythagorean theorem, we have: R 2 \u003d AB 2 \u003d AC 2 + BC 2 \u003d 2 2 + 2 2 \u003d 8.

Now we find the area of the circle and the sector: S of the circle = πR 2 = 8π; S = 0.25 S circle = 2π.

Finally, the desired value is equal to S /π = 2.

Sector area with unknown radius

This is a completely new type of task, there was nothing like it in 2010-2011. By condition, we are given a circle of a certain area (namely, the area, not the radius!). Then, inside this circle, a sector is allocated, the area of which is required to be found.

The good news is that these problems are the easiest of all the problems in the square, which are in the exam in mathematics. In addition, the circle and sector are always placed on the coordinate grid. Therefore, to learn how to solve such problems, just take a look at the picture:

Let the original circle have area S of the circle = 80. Then it can be divided into two sectors of area S = 40 each (see step 2). Similarly, each of these "half" sectors can be divided in half again - we get four sectors of area S = 20 each (see step 3). Finally, you can divide each of these sectors into two more - we get 8 sectors - "little pieces". The area of each of these "chunks" will be S = 10.

Please note: there is no smaller division in any USE task in mathematics! Thus, the algorithm for solving problem B-3 is as follows:

Cut the original circle into 8 sectors - "pieces". The area of each of them is exactly 1/8 of the area of the entire circle. For example, if according to the condition the circle has the area S of the circle = 240, then the “lumps” have the area S = 240: 8 = 30;
Find out how many "lumps" fit in the original sector, the area of which you want to find. For example, if our sector contains 3 “lumps” with an area of 30, then the area of the desired sector is S = 3 30 = 90. This will be the answer.

That's all! The problem is solved practically orally. If you still don't understand something, buy a pizza and cut it into 8 pieces. Each such piece will be the same sector - "chunk" that can be combined into larger pieces.

And now let's look at examples from the trial exam:

A task. A circle with an area of 40 is drawn on checkered paper. Find the area of the shaded figure.

So, the area of the circle is 40. Divide it into 8 sectors - each with an area of S = 40: 5 = 8. We get:

Obviously, the shaded sector consists of exactly two "small" sectors. Therefore, its area is 2 5 = 10. That's the whole solution!

A task. A circle with an area of 64 is drawn on checkered paper. Find the area of the shaded figure.

Again, divide the entire circle into 8 equal sectors. Obviously, the area of one of them just needs to be found. Therefore, its area is S = 64: 8 = 8.

A task. A circle with an area of 48 is drawn on checkered paper. Find the area of the shaded figure.

Again, divide the circle into 8 equal sectors. The area of each of them is equal to S = 48: 8 = 6. Exactly three sectors-“small” are placed in the desired sector (see figure). Therefore, the area of the desired sector is 3 6 = 18.