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Arc length

Maths: Edexcel A Level Pure Maths, topic 5.1.2

Arc Length of a Sector

We can find the arc length of a sector of a circle given the radius of the circle and the angle of the sector.

Arc length

Arc length

  • The length of the arc of a sector of a circle is equal to the radius rr multiplied by the angle θ:
  • s=rθs = r\theta
  • Where the angle θ is measured in radians.
Example

Example

  • What is the arc length, ss, of the sector with angle θ=2π5\theta = \frac{2\pi}{5} radians and radius 4.5 cm?
Arc length

Arc length

  • The equation for arc length is s=rθs = r\theta.
  • Substituting in, we get:
  • s=4.5×2π5=9π5=5.65s = 4.5 \times \frac{2\pi}{5} = \frac{9\pi}{5} = 5.65 cm (2 d.p.)

Test yourself on Arc length

  • What is the equation for the arc length of a sector?

  • What is the arc length of a sector with angle π\pi and radius rr equal to?

Practise this topic for free