Question

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find: (i) length of the arc. (ii) area of the sector formed by the arc. (iii) area of the segment formed by the corresponding chord.




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Answer 1

Answer:

$In the mentioned figure,</p><p></p><p>O is the centre of circle,</p><p></p><p>AB is a chord</p><p></p><p>AXB is a major arc,</p><p></p><p>OA=OB= radius =21 cm</p><p></p><p>Arc AXB subtends an angle 60o at O.</p><p></p><p></p><p>i) Length of an arc AXB =36060×2π×r</p><p></p><p></p><p>                                          =61×2×722×21</p><p></p><p></p><p>                                          =22cm</p><p></p><p></p><p> ii) Area of sector AOB =36060×π×r2</p><p></p><p></p><p>                                         =61×722×(21)2</p><p></p><p></p><p>                                         =231cm2</p><p></p><p></p><p>iii) Area of segment (Area of Shaded region) = Area of sector AOB− Area of △AOB</p><p></p><p></p><p>By trigonometry,</p><p></p><p>AC=21sin30</p><p></p><p>OC=21cos30</p><p></p><p>And, AB=2AC</p><p></p><p>∴ AB=42sin30=41×21=21 cm</p><p></p><p></p><p>∴ OC=21cos30=2213 cm</p><p></p><p></p><p>∴ Area of △ AOB =21×AB×OC</p><p></p><p></p><p>                              =21×21×2213=44413 cm2</p><p></p><p></p><p>∴ Area of segment (Area of Shaded region) =(231−44413)  cm2</p><p></p><p>$

Answer 2

Answer:

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