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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

= 12 × 2 π r

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

Question Image

Solving further,

= 72 π + 32 π + 5 π = 5 π + 5 π = 10 π = 31.4 cm

So, the perimeter of the shaded region is

31.4 cm .

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?