Composite Figures, SM-Bank 015

Vinnie cuts away two-thirds of a circle, leaving the shape shown below.

If the circles' radius is 10 cm, what is the perimeter of the remaining shape, to the nearest centimetre? (2 marks)

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\( 41\ \text{cm (nearest cm)}\)

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\(\text{Fraction of circle}=\dfrac{360-240}{360}=\dfrac{120}{360}=\dfrac{1}{3}\)

\(\text{Perimeter}\)	\(=2\ \text{radii}+\dfrac{1}{3}\times \text{circumference}\)
	\(=2\times 10 +\Bigg(\dfrac{1}{3}\times 2\pi\times r\Bigg)\)
	\(=20 +\Bigg(\dfrac{1}{3}\times 2\pi\times 10\Bigg)\)
	\(=20+\dfrac{20\pi}{3}\)
	\(= 40.943\dots\)
	\(= 41\ \text{cm (nearest cm)}\)