Question

30] The shaded region ABCD shows the space enclosed by two concentric
circles with centre 'O' and the angle at the centre is 75° If the radii of
the circles are 21 cm and 42 cm, find the area of the shaded region and
the perimeter of ABCD

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Answer 1

Step-by-step explanation:

area of shaded region = area of the sector - area of smaller sector

= πr1^2/360° × 75° - πr2^2/360° × 75°

= π(42)^2/360° × 75° - π(21)^2/360° × 75°

= 1155 - 288.75

= 866.25cm2

perimeter = 21 + 21 + 2πr1 × 75°/360° + 2πr2 × 75°/360°

= 42 + 2π × 75°/360° (r1+r2)

= 42 + 1.31 ( 42 + 21 )

= 42 + ( 1.31 × 63 )

= 42 + 82.47

= 124.47

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