The circle represents the locus of points in the plane that are equidistant from a single center of the circle. The radius of the segment that connects the center of the circle with any of her points. To determine the radius of the circle, do not require heavy algebraic operations.
Instruction
1
Let L be the length of the circumference, π a constant, the value of which is constant (π=3.14). Then, to determine the radius given the circumference, you need to use the formula:
R = L/2π
Example: length of a circle is 20 cm. Then the radius of this circle R = 20/2*3.14 = 3.18 cm
2
Let the famous S - area of a circle. Then, knowing the formula for finding the area of a circle (S = πR2), it's easy to withdraw and another to determine the radius of a circle:
R = √(S/π)
Example: area of a circle is 100 cm2, then its radius is R = √(100/3.14) = 5.64 cm
3
If the circumference length of the diameter (a line segment which connects two opposite points of the circle, passing through its center), the task of finding the radius is to divide the length of the diameter of the circle by 2.
Note
Besides the fact that the circle has radius and diameter, it can be constructed chord, Central angle, and inscribed angle. A chord is a segment connecting the 2 points of the circle not passing through its center.

The Central angle is a angle whose apex coincides with the center of the circle. The same inscribed angle is an angle whose vertex lies on any point of the circle.

A circle can also be described around some geometric shapes, or inscribed in it. A circle can be described around an equilateral triangle, square or any other regular polygon. To inscribe a circle in any of these figures.
If circle is inscribed in an equilateral triangle, a square or another polygon, the radius of this circle equals the square of the polygon is half its perimeter:
R = S/p.

If a circle circumscribed around a triangle, then its radius is set according to the formulas:
R=(a*b*c)/(4*S), where a, b, c be the sidelengths of a triangle, S is the area of the triangle;
R = a/2*sinα, where α is the angle opposite side a.

# Advice 2 : How to find the radius of the circle

The word radius radius translates from Latin as "spoke wheels, ray." A radius is any line segment that connects the center of a circle or sphere with any point lying on this circle or on the surface of this sphere, and also the length of this segment is the radiusom. To denote the radiusand the computing and mathematical expressions using the Latin letter R.
Instruction
1
The diameter of a circle is a line segment that passes through the center of the circle and connects two most distant between a point lying on the circumference. The length of this segment is also called a diameter of the circle. The radius is half the diameter of a circle, so if you know the diameter of this circleto find its radius by dividing it in half. R = D/2 where D is the diameter of the circle.
2
The length of the curve, forming a circle on a plane is the length of the circumference. If the known length of a circle you can use the formula: R = L/2?, where L is the length of the circle, ? is a constant equal 3,14159... Constant ? equal to the ratio of the length of the circumference to the diameter, this value is the same for all circles.
3
A circle is a geometric figure that represents the portion of the plane bounded curve is a circle. If you know the area of a circle, find the radius of a circle from the following formula: R = v(S/?), where v is the square root, S – the area of a circle.
Note
The radius of the circle is the positive value not equal to zero.

# Advice 3 : How to calculate the radius of the circle

Ancient geometry based on multiple mathematical operations with a circle, circumference and diameter was derived universal PI. PI is ratio of circle's circumference to its radius with a numeric value of approximately 3.14.
You will need
• knowledge and skills mathematics
Instruction
1
Often in life a situation may arise when a given approximate land area necessary to issue a simple form of the circle. For example, it can be huge flower beds on city squares and in parks. Yes, and beds are smaller in the suburban area, it is desirable to plan through geometry. No wonder the name of this science is translated as the measurement of the earth.To delineate the boundaries of a designated area, do first a simple mathematical calculation.
2
To do this, take the formula for area of a circle: S =πR2. Here S is the area of the circle,π is 3.14,R is the radius.To calculate the radius of a circle, convert the given formula for area of a circle, moving the symbol radius in the left part of equality. Thus, the radius will be equal to the square root extracted from the private area of a circle and the number π.R = v-s/proverite formula with a specific example. Suppose you have a stipulated area of 1,000 sq. m. Substitute in the formula a numeric value.R = v-1000 : 3.14 = v--318.47 = 17.9 m. the Radius of a circle with an area of 1000 sq. m. will be 17 m. 90 cm.
3
The following situation, when you know the value of the circumference of the plot.In this case, the radius count for формулеL = 2nr where L is the length of the circumference. Hence: R = L/2пПодставив numerical values, we get:R = 1000/2*3.14 = 159.2 m. That is, the radius of a circlehaving a circumference of 1000 m, will be 159 m. 20 cm.
A small circle can be drawn with twine and tied on a distance of the length of the radius of the two stakes. One of them goes in the center, the other outlines the boundary of the circle.

The radiusis a parameter that determines the exact size of the circle or sphere, a knowledge of it alone is enough to build such geometric shapes. The radius associated with relatively simple correlations with other characteristics of rounded geometric figures - perimeter, area, volume, surface area etc. This allows a simple calculation to find the radius based on indirect evidence.
Instruction
1
If you want to calculate the radius (R) of a circle, the perimeter (P) which is given in the source terms, divide the circumference - the perimeter is to double the number PI: R = P/(2*π).
2
Area (S) of the plane bounded by a circle can also be expressed through the radius (R) and the number PI. If known, remove square root from the ratio between the area and the number PI: R = √(S/π).
3
Knowing the arc length (L), i.e. of the perimeter of the circle and the corresponding Central angle (α) is the radius of the circle (R) to calculate also possible. If the Central angle in radians, just divide it on the length of the arc: R = L/α. If the angle is given in degrees, the formula is much more complicated. Multiply the arc length of 360°, and the result divide by twice the product of PI to the size of the Central angle in degrees: R = 360*L/(2*π*α).
4
It is possible to Express the radius (R) and using the chord length (m) connecting the extreme points of the arc, if measured in degrees the angle (α) that forms the sector of a circle. Divide the half chord length by the sine of half the angle: R = m/(2*sin(α/2)).
5
If you need to calculate the radius (R) sphere, inside of which is enclosed known volume of space (V), will have to calculate the cube root. As a radical expression, use triple the amount divided by four PI: R = 3√(3*V/(4*π)).
6
Knowledge of the surface area of the sphere (S) also allow to calculate the ball's radius (R). To do this, extract the square root of the ratio between the area and quadrupled the number PI: R = √(S/(4*π)).
7
Knowing the entire area of the sphere, but only the area (s) of its part - segment of a given height (H), it is also possible to calculate the radius (R) three-dimensional figures. Half the area of the segment, divide by the product of the height by PI: R = √(s/(2*π*H)).
8
The simplest is to calculate the radius (R) according to the known diameter (D) of the figure. Divide this value in half and get the required value as for the circle and sphere: R = D/2.
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