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

hintHint:

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 = straight pi (r1)2
    = 3.14 × (3.5)2 = 38.465 cm2
    Area of semi-circle OACB = 1 half × r2
    = 1 half × 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 = 1 half × b × h  = 1 half × AB × OC
    = 1 half × 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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