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Question
In the following 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 = 7 cm, find the area of the shaded region.
Solution
It is given that AB and CD are two diameters of a circle perpendicular to each other and OD is the diameter of small circle.
It is given that, `OA=7 cm`
So, radius r of small circle is
`r=7/2 cm`
` =3.5 cm`
We know that the area A of circle of radius r is`A=pir^2`.
Substituting the value of r in above formula,
`A=22/7xx3.5xx3.5`
`=154 cm^2`
Hence,
`"Area of shaded region= Area of large circle -Area of small circle"`
`=145-38.5`
`=115.5 cm^2`
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