Arcs & Sectors (Cambridge O Level Maths)

What is an arc?

• An arc is a part of the circumference of a circle 
• Two points on a circumference of a circle will create two arcs 
  • The smaller arc is known as the minor arc
    
  • The bigger arc is known as the major arc

What is a sector?

• In technical terms, a sector is the part of a circle enclosed by two radii (radiuses) and an arc
• It’s much easier to think of a sector as the shape of a slice of a circular pizza (or cake, or pie, or …) and an arc as the curvy bit at the end of it (where the crust is)
• Two radii in a circle will create two sectors
  • The smaller sector is known as the minor sector
    
  • The bigger sector is known as the major sector

• If the angle of the slice is θ (the Greek letter “theta”) then the formulae for the area of a sector and the length of an arc are just fractions of the area and circumference of a circle:
  • Remember that a full circle is equal to 360° so the fraction will be the angle, out of 360

• If you are not too good at remembering formulae there is a logic to these two
  • You’ll need to remember the circumference and area formulas
  • After that we are just finding a fraction of the whole circle – “θ out of 360”
• Working with sector and arc formulae is just like working with any other formula
  • WRITE DOWN – what you know (what you want to know)
  • Pick correct FORMULA
  • SUBSTITUTE and SOLVE