Q17 of 49 Page 1

In Fig. 4, AB and CD are two diameters of a circle with centre O, which are perpendicular to each other. OB is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region. [use π = 22/7]

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Fig.4

Given-

AB and CD are the diameters of bigger circle with centre O and OA = 7 cm.


∴ Radius of Bigger Circle(R) = 7 cm


Radius of Smaller Circle(r) = (7/2) cm


Area of Δ ADC = (1/2) × Base× Corresponding Altitude


= (1/2) × CD× OA


= (1/2) × 14× 7


= 49 sq. cm


Area of Semicircular Region CAD = (1/2) × Area of Bigger Circle


= (1/2) × π × (R)2


= (1/2) × (22/7) × (7)2


= 77 sq. cm


Area of Smaller circle = π × (r)2


= (22/7) × (7/2)2


= (77/2)


= 38.5 sq. cm


Thus, Area of Shaded Region


= Area of Smaller circle+ Area of Semicircular Region CAD- Area of ΔADC


= 38.5 + 77 - 49


= 66.5 sq. cm


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