Composite Figures, SM-Bank 028

Pixie is designing a new company logo. The design is made up of three identical sectors with the radius of each sector being 18 millimitres.

Calculate the perimeter of Pixie's. Give your answer correct to the nearest millimetre. (3 marks)

NOTE: \(\text{Arc length: }l=\dfrac{\theta}{360}\times 2\pi r\)

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\(127\ \text{cm (nearest mm)}\)

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\(\text{Radius of sector}\ r=18\ \text{mm, Sector angle }\theta=60^\circ\)

\(\text{Perimeter}\)	\(=6\ \text{straight edges}+3\times \text{arc length}\)
	\(=6r+\Bigg(\dfrac{\theta}{360}\times 2\pi r\Bigg)\)
	\(=6\times 18+\Bigg(\dfrac{60}{360}\times 2\pi\times 18\Bigg)\)
	\(=108 +\Bigg(\dfrac{60\times 36\pi}{360}\Bigg)\)
	\(=108+6\pi\)
	\(=126.849\dots\)
	\(\approx 127\ \text{cm (nearest mm)}\)