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Circular sector

 

 
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Circular sector
 
 
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A circular sector or circle sector, is the portion of a circle
Circle

A circle is a simple shape of Euclidean geometry consisting of those point in a plane which are the same distance from a given point called the center....
 enclosed by two radii
RADIUS

Remote Authentication Dial In User Service is a networking protocol that provides centralized access, authorization and accounting management for people or computers to connect and use a network service....
 and an arc
Arc (geometry)

In geometry, an arc is a closed set segment of a differentiable curve in the two-dimensional manifold; for example, a circular arc is a segment of the circumference of a circle....
, where the smaller area is known as the minor sector and the larger being the major sector. Its area can be calculated as described below.

Let θ be the central angle
Central angle

A central angle is an angle whose vertex is the center of a circle, and whose sides pass through a pair of points on the circle, thereby subtending an Arc between those two points whose angle is equal to the central angle itself....
, in radian
Radian

The radian is a unit of plane angle, equal to 180/pi Degree , or about 57.2958 degrees, or about 57?17'45?. It is the standard unit of angular measurement in all areas of mathematics beyond the elementary level....
s, and the radius. The total area of a circle is . The area of the sector can be obtained by multiplying the circle's area by the ratio of the angle and (because the area of the sector is proportional to the angle, and is the angle for the whole circle):

Also, if refers to the central angle in degree
Degree (angle)

A degree , usually denoted by ? , is a measurement of plane angle, representing 1/360 of a Turn ; one degree is equivalent to p/180 radians....
s, a similar formula can be derived.

Sectors can have special relationships, which include halves
One half

One half is the irreducible fraction resulting from dividing 1 by 2 , or any number by its double; multiplication by one half is equivalent to division by two....
, quadrant
Quadrant

Quadrant may refer to:* One of the four sections of the Cartesian coordinate system#Two-dimensional coordinate system* Quadrant , a measuring instrument capable of measuring angles up to 90°...
s, and octant
Octant

An octant is one of eight divisions....
s.

The length, , of the arc of a sector is given by the following formula:



where θ is in degrees.

The length of the perimeter
Perimeter

A perimeter is a path that bounds an area. The word comes from the Greek peri and meter . The term may be used either for the path or its length....
 of a sector is sum of arc length and the two radii.






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Encyclopedia


A circular sector or circle sector, is the portion of a circle
Circle

A circle is a simple shape of Euclidean geometry consisting of those point in a plane which are the same distance from a given point called the center....
 enclosed by two radii
RADIUS

Remote Authentication Dial In User Service is a networking protocol that provides centralized access, authorization and accounting management for people or computers to connect and use a network service....
 and an arc
Arc (geometry)

In geometry, an arc is a closed set segment of a differentiable curve in the two-dimensional manifold; for example, a circular arc is a segment of the circumference of a circle....
, where the smaller area is known as the minor sector and the larger being the major sector. Its area can be calculated as described below.

Let θ be the central angle
Central angle

A central angle is an angle whose vertex is the center of a circle, and whose sides pass through a pair of points on the circle, thereby subtending an Arc between those two points whose angle is equal to the central angle itself....
, in radian
Radian

The radian is a unit of plane angle, equal to 180/pi Degree , or about 57.2958 degrees, or about 57?17'45?. It is the standard unit of angular measurement in all areas of mathematics beyond the elementary level....
s, and the radius. The total area of a circle is . The area of the sector can be obtained by multiplying the circle's area by the ratio of the angle and (because the area of the sector is proportional to the angle, and is the angle for the whole circle):

Also, if refers to the central angle in degree
Degree (angle)

A degree , usually denoted by ? , is a measurement of plane angle, representing 1/360 of a Turn ; one degree is equivalent to p/180 radians....
s, a similar formula can be derived.

Sectors can have special relationships, which include halves
One half

One half is the irreducible fraction resulting from dividing 1 by 2 , or any number by its double; multiplication by one half is equivalent to division by two....
, quadrant
Quadrant

Quadrant may refer to:* One of the four sections of the Cartesian coordinate system#Two-dimensional coordinate system* Quadrant , a measuring instrument capable of measuring angles up to 90°...
s, and octant
Octant

An octant is one of eight divisions....
s.

The length, , of the arc of a sector is given by the following formula:



where θ is in degrees.

The length of the perimeter
Perimeter

A perimeter is a path that bounds an area. The word comes from the Greek peri and meter . The term may be used either for the path or its length....
 of a sector is sum of arc length and the two radii. It is given by the following formula:



where θ is in degrees.

See also

  • Circular segment
    Circular segment

    In geometry, a circular segment is an area of a circle informally defined as an area which is "cut off" from the rest of the circle by a secant line or a chord ....
     - the part of the sector which remains after removing the triangle formed by the center of the circle and the two endpoints of the circular arc on the boundary.
  • Conic section
    Conic section

    File:Conic sections with plane.svgIn mathematics, a conic section is a curve obtained by intersecting a cone with a plane . A conic section is therefore a restriction of a quadric surface to the plane ....


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