2.2 Area of Sectors and Segments

Note: if you cannot remember how to calculate values of a circle, review notes for 2.1 Circles and Arcs.

Area of a Sector

  • The area of a circle sector can be found by multiplying the formula for the area of a regular circle by the fraction of the circle which the sector encompasses. The angle is used for this fraction:

A=\frac{\pi r^{2} \theta}{360}

Where A is the area of the sector, r is the radius of the sector and θ is the angle of the sector.


Picture 2

Above is a diagram of a machine component which is manufactured by cutting a 45o sector out of circle of radius 15mm. The company making these parts wishes to know the area of material which is wasted (cut out) per component. To do this we will use our area formula:

A=\frac{\pi r^{2} \theta}{360}=\frac{\pi 15^{2} 45}{360}=88.36 m m^{2}


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2.1 Circles and Arcs


  • The set of all points in the plane that are a fixed distance (the radius, r) from a fixed point (the centre, O).
  • The angle at the centre of a circle is 360°.

Diameter (D)

  • A chord passing through the centre.
  • D = 2r, twice the length of the radius.

Circumference of a Circle

  • The circumference of a circle, AKA the perimeter, is given by:

c=2 \pi r

Read More »2.1 Circles and Arcs