## "Taught in school, teach in school..."

Curriculum the sixth grade students of secondary schools in the geometry course studying the circle and the circle as a geometric figure, and this figure is due. The kids are introduced to such concepts as the radius and the diameter, the circumference or perimeter of a circle, area of a circle. It is on this topic they learn about the mysterious number PI is rudolfova number, as it was called before. The number PI is irrational because its decimal is infinite. In practice it is used a truncated version of the three digits: 3.14. This constant expresses the ratio of any circle's circumference to its diameter.

Sixth graders solve problems, bringing one of the given and the "PI" of the other characteristics of a circle and circle. In notebooks and on the chalkboard they scale drawing abstract sphere and produce little that speakers of calculations.

## But in practice

In practice, this problem can occur when, for example, there is a need to pave the road to a certain extent for the conduct of any events with a start and finish in one place. Calculate the radius, you can plan to choose the passage of this route, with compass in hand considering the options, taking into account geographical features of the region. Moving leg of a compass – equidistant from center of the future alignment at this stage to anticipate where the areas are lifts, where the slopes, given the natural variations of the terrain. Also you can define the areas where to place the stands for fans.

## The radius of the circle

So, suppose that you are for competition autocross necessary circular track with a length of 10 000 m. this is the correct formula for determining the radius (R) of a circle with known length (C):

R=C/2P (p – a number equal to 3.14).

Substituting the available values, you can easily get the result:

R = 10 000:3.14 = 3 184. 71 (m) or 3 km 184 m and 71 cm.

## From the radius to the square

Knowing the radius of the circle, it is easy to determine the area that will be removed from the landscape. The formula of circle area (S): S=пR2

When R = 3 184. 71 m it will be: S = 3.14 x 3 184. 71 x 3 184. 71 = 31 847 063 (sq. m), or nearly 32 square kilometers.

Similar calculations can be useful for fencing. For example, you have material on the fence for so many meters. Taking this value for the perimeter of the circle, you can easily determine the diameter (radius) and area (and therefore visibly present value of the future fenced area.

# Advice 2 : How to calculate the circumference

Circle - a geometric figure that is drawn on a plane. Is the circumference of the plurality of points that are equidistant from a given center. In order to calculate its

**length**, you can apply multiple formulas.You will need

- You will need the following values:
- R - length of radius of the circle;
- D - the length of the diameter of a circle;
- π is a constant (π = 3.14)

Instruction

1

Method 1. Let the plane of a circle. Its radius is equal to R. Then

L = 2nr.

Example: the Radius

**the length**L of this**circle**is considered thus:L = 2nr.

Example: the Radius

**of the circle**R = 5 cm Then the length of**circumference**L = 2*3.14*5 = 31.4 cm2

Method 2. Given a circle with diameter D. Then L is:

L = πD.

Example: the Diameter

L = 3.14*10=31.4 cm

L = πD.

Example: the Diameter

**of a circle**D = 10 cm Then L is calculated as:L = 3.14*10=31.4 cm

Note

The answers in the first and second method are equal, because the length of the radius equal to half the length of the diameter of the circle.

# Advice 3 : How to find the diameter

**The diameter**is a line that connects two points a curved shape and passes through its center. In many applied problems it is required to find the diameter of a circle or sphere.

**The diameter**of a circle to find its radius, length and area of a circle.

**The diameter**of the ball find the radius, volume and surface area.

Instruction

1

**The diameter**of a circle or sphere, if their radii can be found, knowing that the diameter is two times the radius. Thus, for finding the diameter and radius, have radius multiplied by two:

D = 2*R, where R is the radius of the shape.

2

**The diameter**of a circle if you know its length can be found by the formula:

D = L/PI where L is the circumference, PI is a constant approximately equal to 3.14.

3

**The diameter**of a circle if you know its area, you can find the formula:

D = 2*(S/PI)^1/2, where S is the area of a circle.

4

**The diameter**of the ball, if known, its volume can be find using the formula:

D = (6V/PI)^1/3, where V is the volume of a sphere.

5

If you know the surface area of a sphere, its diameter can be determined by the formula:

D = (S/PI)^1/2, where S is the surface area of a sphere.

D = (S/PI)^1/2, where S is the surface area of a sphere.

Note

^ is a sign indicating exponentiation;

^1/2 is actually the square root;

^1/3 is the cube root extraction.

^1/2 is actually the square root;

^1/3 is the cube root extraction.

# Advice 4 : How to calculate the diameter of a circle

As a rule, in problems of geometry, as well as in practical Affairs, is set to

**the diameter****of a circle**and want to find its length. But there are times when you need the opposite — the known length**of the circumference**and we must calculate the remaining parameters. In math class or sketching, you may need to know the radius**of the circle**, before it is drawn. In practical life also there are times. For example, you know the size of the hat and want to build her pattern.You will need

- The compass
- The concept of radius, diameter and circumference
- The formula for the circumference of a circle

Instruction

1

Remember what the length

**of the circumference**and how is it measured. In practical life this is usually used flexible measuring devices like a tape or tape measure. If you need to know**the diameter of the**cylinder base, you can make it scan, circling the base and building side surface. The length**of the circumference**of the base in this case will be equal to the length of the base.2

Remember, what is the formula to calculate the length of the

**circumference**. Indicate the length**of a circle**With radius as R,**the diameter**— as D. the Length**of a circle**is equal to twice the product of the radius by the number ?, C=2?R. Remember what**the diameter****of the circle**. This is twice the radius.3

Find twice the radius

**of the circle**. 2R=C/?. Thus, D=C/?. Remember, what is the number ?. It is equal to 3, 14. Divide the length**of the circumference**by this number. To determine the necessary radius of the resulting quotient divided by 2. Will watertite a circle according to the obtained radius.4

Knowing the length of the radius, one can determine the area of a circle. You must do this if making a pattern round the hat, you want to calculate. How much material is needed. Indicate the area of the circle as S. It will be equal to the number ?, multiplied by the square of the radius.

Note

The number p is an infinite decimal. It is usually rounded off to two digits after the decimal point.

The radius is calculated to the required accuracy. If it turns out an infinite decimal, it is interrupted in the hundredths or tenths and rounded.

The radius is calculated to the required accuracy. If it turns out an infinite decimal, it is interrupted in the hundredths or tenths and rounded.

# Advice 5 : How to find the radius of the circle

The definition

**of the radius****of the circle**is one of the main tasks of mathematics. There are many formulas to account for the**radius**, you just know some standard options. Graphically, the radius is denoted by letter R in the Latin alphabet.Instruction

1

A circle is a closed curve. The points that lie in its plane, equidistant from the centre, which lies in one plane together with a curve. Radius - a segment

**of a circle**connecting its center with any point. With its help, you can learn many other parameters of the figure, so it is a key parameter. The numerical value**of the radius**will be the length of this segment.2

You should also distinguish the radius of the shape from its diameter (diameter connects the two most remote from each other point). To use a mathematical method of finding

**the radius**you need to know the length or diameter**of the circle**. In the first case the formula will look like R = L/2?", where L is the known length**of the circumference**, and the number ? equal to 3.14 and is used to denote a particular irrational number.3

In the case that the only known diameter, the formula will look like R = D/2".

4

If the length

**of the circle**is unknown, but there are data on the length and height of a segment, the formula would be R = (h^2*4 + L^2)/8*h where h is the height of the segment is the distance from mid-chord to the most protruding part of the said arc) and L is the length of the segment (which is not the chord length).Chord – a line segment that connects two points**of a circle**.Note

It is necessary to distinguish the concept of "circumference" and "circle". The circle is part of the plane, which, in turn, is limited by the circumference of a certain radius. To find the radius, you must know the area of a circle. In this case, the equation would be R = (S/π)^1/2, where S is a square. To calculate the area, in turn, should know the radius (S = NR^2").

# Advice 6 : How to find the circumference of a circle

Such geometrical figures as the circle, there are several characteristics: radius, diameter, area, length

**of a circle**. They are all interrelated. This means that any of them concluded enough information to determine all the other characteristics of the same**circle**.Instruction

1

A circle is a curve bounding a plane, called the circle. In other words, the circumference is called the locus of points in the plane equidistant from the centre. Segments connected to a center

**of a circle**are called its radii, and the distance from one point to another passing through the centre is called a diameter**of the circle**. The diameter**of a circle**equal to twice the radius: D=2r. The equation**of a circle**in analytic geometry is:x^2+y^2=R^2Существует also the concept of the chord**of the circle**. It is also obtained by connecting two points**of the circle**, but not necessarily passes through its center. All the diameters that pass through the middle of the chord perpendicular to it. The biggest chord**of a circle**is its diameter.2

As with any curve, a circle has a certain

*length*p. It has long been observed that the length**of a circle**relates to its diameter the number PI:p/d=patsada it follows that p=πd, or p = 2nr, where r is the radius**of the circle**.The number π is an irrational value, but it is approximately equal to 3.14.Knowing*the length***of the circumference**, and determine the area of the ring bounded by two circles. It is equal to:S=2nr*k, where k is the distance between the inner and outer circumferences of the ring; 2nr - length internal**circumference**of the ring.3

Graphical way to determine the length of

**the circumference**, because of its inaccuracies, is rarely used. For this purpose an odometer is a device for measuring the length of a curve. Anywhere**circles**mark the start point of the measurement. To bring her odometer, and lead him along the line until it gets to the same point.4

The definition of the length

**of the circumference**has considerable practical value. In addition to mathematicians, it is necessary to carry out physicists, astronomers. First calculate*the length***of the circumference**of elementary particles, the second of the heavenly bodies. Also, knowing the diameter of the circus arena, a running track, guided by the above formulas, we can calculate what distance they will run a horse or runner at a range.# Advice 7 : The diameter of a circle: how to define it

With a circumference associated with many interesting, beautiful and difficult theorems in geometry. Our task is one of the most simple: we have to find

**diameter****of a circle**. Will try to do it using two formulas.Instruction

1

A segment that connects any two points of a circle is called a chord.Passing through the center of a circle, the chord is called its diameter. The diameter denoted by the symbol or Latin letter D. Diameter (D) twice as long as the radius of curvature (R) and is the greatest possible distance between the points on the circle.Example. The radius of the circle is 20 cm D(diameter)? Then, if R = 20 cm and we know that the length of the diameter equal to the length of the two radii D = 2R = 2*20 = 40 cm

2

There is a second way to find the diameter of a circle. In this case, we should be known for its length. Mark the circumference of the Latin letter C. Example. C = 60 cm D - ? Solution. From geometry we know that the circumference is given by: C = 2R, where: R is the radius of the circle, and is an irrational number "PI" equal approximately to 3.14. Then, this formula implies the other: D = With : 3,14. So, D = 60 : 3,14 = 19,12 see

Useful advice

A circle is sometimes called the "wheel geometry". One of the properties of the wheel, its axis remains all the time at a constant distance from the surface on which it rolls in the mathematical formulation becomes the definition of the circle. Circle is the set of points in the plane, distant from a fixed point, its centre, the same distance, or radius (from Latin radius "spoke wheels", "ray"). Radii are also called line segments connecting the center points of the circle.

The diameter divides the circumference into equal parts. Commenter "Started" the ancient Greek philosopher Proclus, who lived in the V century, attributed this discovery to Thales, the acknowledged founder of ancient philosophy and science. Clarifying this statement, we can say that a circle symmetric about any diameter (or rather, its containing straight).*

* Encyclopedia for children, volume 11 of Mathematics, Moscow, "AVANTA+", 1998.

The diameter divides the circumference into equal parts. Commenter "Started" the ancient Greek philosopher Proclus, who lived in the V century, attributed this discovery to Thales, the acknowledged founder of ancient philosophy and science. Clarifying this statement, we can say that a circle symmetric about any diameter (or rather, its containing straight).*

* Encyclopedia for children, volume 11 of Mathematics, Moscow, "AVANTA+", 1998.

# Advice 8 : How to calculate the radius of the circle

To calculate the radius of the circle, enough to know the radius of this circle, as well as the necessary constant values. Consider two options compute the circumference of a circle that involve different constant values.

Instruction

1

For starters, understand the terms and definitions with which you have to work with. Note that a circle is a figure consisting of all points in the plane, for each of which the ratio of distances to two given points is equal to this number, different from unity. Radius is not only the value of the distance, but the segment that connects the center of the circle with one of its points. The circumference is the value of the segment AB consists of points A, b, and all points in the plane from which the segment AB is seen under a right angle from the diameter. PI is an irrational number, then there is a never ending and non-periodic and which is the length of the semicircle, the radius of which is equal to one, the number PI is approximately equal to 3.14.

2

So, according to the first method, to calculate the radius of the circle is possible, if you know the radius of the circle. To do this, multiply the length of the radius by PI, approximately equal to 3.14, and in figure 2. In other words, the standard formula calculation of the radius of the circle is: L = 2 x P x R, where L is the circumference, N is the number PI (~3,141592654), R is the radius of the circle. It should be noted that from this formula we can calculate, what is the radius: R = L / (2 x P).

3

There is a shorter formula to find the circumference. The formula is: L = R x alpha, where L is the length of the arc, R is the radius of the circle, alpha is the angle of the arc in radians. A circle is nothing but a closed arc whose angle is 2 x PI radians, so theoretically we again get a formula for the length of the circle L = 2 x PI x R, which indicates the correctness of the formula. It also follows that the number of alpha is also a constant value and is 2 x PI = 6.28 to. Thus, to find the circumference, multiply the radius of this circle is the number of 6.28.

# Advice 9 : How to determine the radius of the circle

A circle is a flat geometric figure, all points of which are at the same non-zero distance from the point indicating the center of this

**circle**. This distance is called**radius**, and its length equals half the diameter - a line segment that connects two points**of circle**and passes through its center. Radius can not be determined knowing only the diameter but also on some other parameters**of the circle**.Instruction

1

If you know the circumference (L), its radius (r) will be determined by the ratio of the circumference to twice the number PI: r=L/(2∗π). For example, if we know the circumference is five meters, the radius can be defined as: 5/(2∗3,14) = 5/6,28 = 79,62 cm.

2

If you know the area

**of a circle**(S), radius (r) can be defined as the square root of the area ratio and the number PI: r=√(S/π). For example, if the area**of a circle**is five square meters, the radius can be calculated as: √(5/3,14) = √1,59 = 1,26 meters.3

If you know the lengths of the sides (a and b) inscribed in a circle of rectangle, radius of circle (r) will be determined as half the diagonal of this rectangle. And since the diagonal length according to the Pythagorean theorem, we can assume the square root of the sum of the lengths of the sides squared, the radius is equal to half of this value: r=0.5∗√(a2 + b2). For example, if the lengths of the known sides equal to two and four meters, the length of the radius can be defined as: 0.5∗√(22 + 42) = 0.5∗√20 = 0.5∗4.47 = 2,24 meters.

4

Practical calculations can be produced, for example, the standard calculator of Windows operating system. The link to the run is placed in one of the subsections of the main menu on the "start" button. Opening it, click All programs, click Accessories, then select system tools and finally, the item "Calculator". An alternative method is to use the run dialog programs that opens by pressing the key combination WIN + R. In this dialogue you can enter the command calc and click the "OK"button.

Note

How to find the radius of the circle? Guénon convenient search of answers to questions. Circle — a closed plane curve, all points of which are equidistant from a given point (center) lying in the same plane as the curve. Circle the part of the plane bounded by a circle. Radius — line segment connecting the center of the circle with any point as well as the length of this segment.

Useful advice

Depending on the conditions of the problem the radius of the circle you can find. Formula 1: R = L / 2π where L is the length of the circle, and π is a constant equal to 3,141 Formula 2: R = √( S / π), where S is the magnitude of the area of a circle. How to find the radius of the circumscribed circle. First, let's define the term itself. The circle described is called when it touches all vertices of the given polygon.