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Circles, SM-Bank 044

Calculate the arc length of the sector below, correct to two decimal places.  (2 marks)

\(l=\dfrac{\theta}{360}\times 2\pi r\)

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\(270.18\ \text{m  (2 d.p.)}\)

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\(\text{Diameter}=172 \text{cm}\)

\(\therefore\ \text{Radius}=\dfrac{172}{2}=86 \text{cm}\)

\(\text{Method 1}\)

\(l\) \(=\dfrac{\theta}{360}\times 2\pi r\)
  \(=\dfrac{180}{360}\times 2\pi \times 86\)
  \(=270.1769\dots\)
  \(=270.18\ \text{m  (2 d.p.)}\)

 

\(\text{Method 2}\)

\(l\) \(=\dfrac{1}{2}\times \text{circumference}\)
  \(=\dfrac{1}{2}\times \pi d\)
  \(=\dfrac{1}{2}\times \pi \times 172\)
  \(=270.1769\dots\)
  \(=270.18\ \text{m  (2 d.p.)}\)