Area, SM-Bank 041

A golf course has a sprinkler system that waters the grass in the shape of a sector, as shown in the diagram below.

A sprinkler is positioned at point \(L\) and can turn through an angle of 100°.

The section of grass that is watered is 4.5 m wide at all points.

Water can reach a maximum of 12 m from the sprinkler at \(L\).

What is the area of grass that this sprinkler will water?

Round your answer to the nearest square metre. (2 marks)

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

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`199\ text{m² (nearest m²)}`

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\(\text{Area}\)	\(=\dfrac{360-\theta}{360}\times \pi\times R^2-\dfrac{360-\theta}{360}\times \pi\times r^2\)
	\(=\dfrac{260}{360}\times \pi\times 12^2-\dfrac{260}{360}\times \pi\times 7.5^2\)
	\(= 199.09\dots\)
	\(= 199\ \text{m² (nearest m}^2)\)