Area, SM-Bank 036

A windscreen wiper blade can clean a large area of windscreen glass, as shown by the shaded area in the diagram below.

The windscreen wiper blade is \(30\) cm long and it is attached to a \(9\) cm long arm.

The arm and blade move back and forth in a circular arc with an angle of \(110^\circ\) at the centre.

Calculate the area cleaned by this blade, in square centimetres, correct to one decimal place. (2 marks)

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

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\(1382.3\ \text{cm}^2\)

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\(\theta=110^\circ,\ \text{Radius large sector}=39,\ \text{Radius small sector}=9\)

\(\text{Area cleaned}\)	\(\ =\ \text{large sector − small sector}\)
	\(=\dfrac{110}{360}\times \pi\times 39^2-\dfrac{110}{360}\times \pi\times 9^2\)
	\(=1382.300\dots\)
	\(\approx 1382.3\ \text{cm}^2\)