In the given figure, OACB is a quadrant of circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the
(i) Quadrant OACB
(ii) Shaded region
[Use Π = 22/7]
(i) Since OACB is a quadrant, it will subtend 90° angle at O.
Area of quadrant OACB = `90^@/360^@ xx pir^2`
`=1/4xx22/7xx(3.5)^2 = 1/4xx22/7xx(7/2)^2`
`= (11xx7xx7)/(2xx7xx2xx2) = 77/8 cm^2`
(ii) Area of ΔOBD = 1/2 x OB x OD
`= 7/2 cm^2`
Area of the shaded region = Area of quadrant OACB − Area of ΔOBD
`= 49/8 cm^2`
Concept: Areas of Combinations of Plane Figures
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