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Question
Find the area enclosed between two concentric circles of radii 3.5 cm and 7 cm. A third concentric circle is drawn outside the 7 cm circle , such that the area enclosed between it and the 7 cm circle is same as that between the two inner circles . Find the radius of the third circle correct to one decimal place.
Solution
The area enclosed between the two circles of radii 3.5 cm and 7 cm
`= pi(7^2-3.5^2)`
`= 115.5 cm^2`
Let the radius of the outermost circle be r cm.
Area betweent the circles with radius r and 7 cm=Area between the circles with radius 7 cm and 3.5 cm
`pi(r^2-7^2)=115.5`
`⇒ (r^2-7^2)=115.5/pi`
`⇒ r^2=36.75+49=85.75 cm^2`
`⇒ r=9.26 cm`
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