A graphic designer is creating a logo that includes a 'shard' element. This shard is defined as the segment of a circle with centre C C\,C and radius 43 cm4\sqrt{3}\text{ cm}43 cm. The segment is bounded by the chord PQ PQ\,PQ and the arc PQPQPQ, where the angle subtended at the centre, ∠PCQ\angle PCQ∠PCQ, is π3\displaystyle \frac{\pi}{3}3π radians.
Show that the area of the shard is k(2π−33) cm2k(2\pi - 3\sqrt{3})\text{ cm}^2k(2π−33) cm2 where k k\,k is an integer to be found.
Practise Edexcel A Level Maths 5.3 Areas of Sectors and Segments with exam-style questions for A Level Maths. 20 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.