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Area, SM-Bank 127

Calculate the area of the following sector, giving your answer as an exact value in terms of \(\pi\).   (2 marks)

NOTE:  \(\text{Sector area}=\dfrac{\theta}{360}\times \pi r^2\)

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\(\dfrac{100\pi}{3}\ \text{m}^2\)

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\(\theta=120^{\circ} \ \ r=10\ \text{m}\)

\(A\) \(=\dfrac{\theta}{360}\times \pi r^2\)
  \(=\dfrac{120}{360}\times \pi\times 10^2\)
  \(=\dfrac{1}{3}\times 100\pi\)
  \(=\dfrac{100\pi}{3}\ \text{m}^2\)