Q18 of 47 Page 1

In Fig. 4, PSR, RTQ and PAQ are three semicircles of diameters 10 cm, 3 cm and 7 cm respectively. Find the perimeter of the shaded region. [Use π = 3.14]


Radius of semicircle RTQ, r1 = 3/2 = 1.5 cm


Radius of semicircle PAQ, r2 = 7/2 = 3.5 cm


Radius of semicircle PSR, r3 = 10/2 = 5 cm


Perimeter of the shaded region = Circumference of semicircle(RTQ + PAQ + PSR)


We know that circumference of semicircle = πr


⇒ Perimeter = πr1 + πr2 + πr3


= π (r1 + r2 + r3)


= 3.14 (1.5 + 3.5 + 5)


= 3.14 (10)


= 31.4 cm


Ans. The perimeter of shaded region is 31.4 cm.


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