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Question
In Fig.5, 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. `[\text{Use}pi=22/7]`
Solution
AB and CD are the diameters of a circle with centre O.
∴ OA = OB = OC = OD = 7 cm (Radius of the circle)
Area of the shaded region
= Area of the circle with diameter OB + (Area of the semi-circle ACDA − Area of ΔACD)
`=pi(7/2)^2+(1/2xxpixx(7)^2-1/2xxCDxxOA)`
`=22/7xx49/4cm^2+1/2xx22/7xx49cm^2-1/2xx14cmxx7cm`
`=77/2cm^2+77cm^2-49cm^2`
`=66.5cm^2`
Thus, the area of the shaded region is 66.5 cm2.
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