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Q.

What will be the perimeter of the shaded region, if in the given figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7cm respectively?


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a

31.4 cm.  

b

31.5 cm.  

c

31.3 cm.  

d

31.2 cm.   

answer is A.

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Detailed Solution

     We have to find the perimeter of the shaded region, if in the given figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7cm respectively.
Calculating the perimeter of the shaded region,
Length of the arc = 1 2 ×2πr  
Perimeter of shaded region = (Length of the arc PAQ) + (Length of the arc PSR) + (Length of the arc RTQ)  Suppose r1,r2,r3,r4 are the radius of arcs PAQ, PSR and RTQ respectively.
Question Image Solving further,
= 7 2 π+ 3 2 π+5π =5π+5π =10π =31.4 cm  
So, the perimeter of the shaded region is 31.4cm.  
Therefore, option 1 is correct.
 
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What will be the perimeter of the shaded region, if in the given figure, PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7cm respectively?