In the figure given below, the boundary of the shaded region comprises of four semicircles two-quarter circles. If OA = OB = OC = OD = 7 cm and the straight lines AC and BD are perpendicular to each other, find the length of the boundary.

68 cm

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49 cm

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66 cm

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44 cm

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Solution

The correct option is C 66 cm
Boundary of shaded region = Circumference of four semicircles (= two circles with r = $\frac{7}{2}$ ) + Circumference of two quarter circles (= one semi-circles with r = 7)
$\Rightarrow (2 π r) + π \times r = (2 \times \frac{22}{7} \times 7) + (\frac{22}{7} \times 7) = 44 + 22 = 66 c m .$

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In the figure given below, the boundary of the shaded region comprises of four semicircles two-quarter circles. If OA = OB = OC = OD = 7 cm and the straight lines AC and BD are perpendicular to each other, find the length of the boundary.

The correct option is C 66 cmBoundary of shaded region = Circumference of four semicircles (= two circles with r = 72) + Circumference of two quarter circles (= one semi-circles with r = 7) ⇒(2πr)+π×r=(2×227× 7)+(227×7)=44+22=66 cm.