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In fig., AB and CD are two diameters of a circle (with centre

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In fig., AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If $O A = 14 c m$ , find the area of the shaded region

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In fig., AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If

O A = 14 c m

, find the area of the shaded region

12 mins ago

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Text solutionVerified

Area of Shaded region

= 2 \times

Area of segment

BC

(or Segment

A C

)

+

Area of circle with diameter

D O

Since,

D O = OC = BO = A O = 7 c m

∴

Area of segment BC

=

Area of quadrant

BOC

-

Area of

△

BOC

= (\frac{π \times 7 \times 7}{4}) - (\frac{1}{2} \times 7 \times 7)

= 14 c m^{2}

Area of circle with diameter

O D

= π \times 3.5 \times 3.5

= 38.5 c m^{2}

∴

Area of Shaded region

= 2 \times 14 + 38.5 = 66.5 c m^{2}

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Question Text	In fig., AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If $O A = 14 c m$ , find the area of the shaded region
Answer Type	Text solution:1
Upvotes	150