Find the area enclosed between two concentric circles, Mathematics

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Find the area enclosed between two concentric circles of radii 3.5cm, 7cm. A third  concentric circle is drawn outside the 7cm circle so that the area enclosed between it and the 7cm circle is same as that between two inner circles. Find the radius of the third circle                                                                                                             (Ans: 115.5 cm 2   r = √343 / 2 )

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Ans:    Area between first two circles = Π x 72 - Π x 3.52

= 49 Π - 12.25 Π -------------(1)

Area between next two circles = Π r2 - Π x 72

= Π r2 - 49 Π -----------------(2)

(1) & (2) are equal

49 Π - 12.25 Π = Π r2 - 49 Π

Π r2 = 49 Π + 49 Π - 12.25 Π

∴ r2 = 98 - 12.25 = 85.75

r2 = 8575/100 = 343/4

r =  √343/2 cm.


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