Question 143

PS is a diameter of a circle of radius 6 cm. In the diameter PS, Q and R are two point such that PQ, QR and RS are all equal. Semicircles are drawn on PQ and QS as diameter (as shown in the figure). The perimeter of shaded portion is:

Solution

It is given that PS = 12 cm

Also, PQ = QR = RS = $$\frac{12}{3}=4$$ cm

Radius of circle having diameter PQ (4 cm) = $$r_1=2$$ cm

Radius of circle having diameter QS (8 cm) = $$r_2=4$$ cm

Radius of circle having diameter PS (12 cm) = $$r_3=6$$ cm

=> The perimeter of shaded portion = $$(\pi r_1)+(\pi r_2)+(\pi r_3)$$

= $$\pi(2+4+6)$$

= $$\frac{22}{7}\times12=\frac{264}{7}=37\frac{5}{7}$$ cm

=> Ans - (C)

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