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Question
In the following figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the (i) quadrant OACB (ii) shaded region.
Solution
It is given that OACB is a quadrant of circle with centre at O and radius 3.5 cm.
(i) We know that the area of quadrant of circle of radius r is,
`A=1/4pir^2`
Substituting the value of radius,`r=3.5 cm^2`
`A=1/4xx22/7xx3.5xx3.5`
`=9.625 cm^2`
Hence, the area of OACB is`.9.625cm^2`
(ii) It is given that radius of quadrant of small circle is 2 cm.
Let the area of quadrant of small circle be .A'
`A'1/4 pir^2`
`=1/4xx22/7xx2xx2`
`=3.14 cm^2`
It is clear from the above figure that area of shaded region is the difference of larger quadrant and the smaller one. Hence,
Area of shaded region=A-A'
`=9.625-3.14`
`= 6.485 cm^2`
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