Find the area of shaded region, if diameters AO, OB, AB are 28 cm, 14 cm, 42 cm, respectively.
[4 marks]
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Solution
Diameters AO, OB, AB are 28, 14, 42 respectively in cm.
Hence corresponding radii will be 14, 7, 21 in cm
( as radius = diameter2)
Area of shaded region
= Area of semicircle with radius 21 cm
+ Area of semicircle with radius 14 cm
+ Area of semicircle with radius 7 cm
We know,
Area of semicircle = 12×pi×r2
Area of semicircle with radius 21 cm
=12×pi×r2= 12×227×212= 22×2122×7= 693 cm2
Area of semicircle with radius 14 cm
=12×pi×r2= 12×227×142= 22×1422×7= 308 cm2
Area of semicircle with radius 7 cm
=12×pi×r2= 12×227×72= 22×722×7= 77 cm2