Arc Lengths & Sector Areas (Cambridge (CIE) IGCSE Maths)

Arc Lengths & Sector Areas

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?

• A sector is the part of a circle enclosed by two radii (radiuses) and an arc

  • A sector looks like a slice of a circular pizza

  • The curved edge of a sector is the arc

• 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

What formulae do I need to know?

• You need to be able to calculate the length of an arc and the area of a sector

• The angle formed in a sector by the two radii is often labelled θ (the Greek letter “theta”)

• You can calculate the area of a sector or the length of an arc by adapting the formulae for the area or circumference of a circle

  • A full circle is equal to 360° so the fraction will be the angle, θ°, out of 360°

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• Working with sector and arc formulae is just like working with any other formula:

  • Write down what you know (or what you want to know)

  • Pick the correct formula

  • Substitute the values in and solve

How do I find the length of an arc?

• STEP 1
  Divide the angle by 360 to form a fraction

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• STEP 2
  Calculate the circumference of the full circle

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• STEP 3
  Multiply the fraction by the circumference

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How do I find the area of a sector?

• STEP 1
  Divide the angle by 360 to form a fraction

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• STEP 2
  Calculate the area of the full circle

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• STEP 3
  Multiply the fraction by the area

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