Maths-
General
Easy
Question
In the given figure, AB and CD are two diameters of a circle perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7cm, find the area of the shaded region
Hint:
Use area of semi-circle OACB to find area of shaded region. Also, note that ABC is forming a triangle.
The correct answer is: 66.395 cm2
It is given that OA = 7 cm
i.e. Radius of bigger circle = 7 cm
Area of shaded region = Area of smaller circle + Area of semi-circle OACB – Area of triangle ABC
Now, OD is radius of bigger circle and diameter of smaller circle
i.e. radius of smaller circle = half of radius of bigger circle
r1 = 3.5 cm
Area of smaller circle = 
(r1)2
= 3.14 × (3.5)2 = 38.465 cm2
Area of semi-circle OACB = 
× r2
= × 3.14 × 72 = 76.93 cm2
AB = diameter of bigger circle = 2 × 7 = 14 cm
OC = radius of bigger circle = 7 cm
Area of triangle ABC = × b × h = × AB × OC
= × 14 × 7 = 49 cm2
Now, Area of shaded region = Area of smaller circle + Area of semi-circle OACB – Area of triangle ABC
= 38.465 cm2 + 76.93 cm2 - 49 cm2
= 66.395 cm2
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