Answer :

Given:

R – r = 7 cm


A – a = 1078 cm2


Where,


R = radii of the larger circle


r = radii of the smaller circle


A = area of the larger circle


a = area of the larger circle


A = πR2


And,


a = πr2


R r = 7


R = 7 + r


Now,


A – a = πR2 – πr2 = 1078


πR2 – πr2 = 1078


π(7 + r)2 – πr2 = 1078


π[(7 + r)2 – r2] = 1078


π[(49 + r2 +14r – r2] = 1078


3.14[(49 + r2 +14r – r2] = 1078


3.14(49 + 14r) = 1078


3.14(49 + 14r) = 1078


3.14 × 7(7 + 2r) = 1078



7 + 2r = 49


2r = 49 7


2r = 42



Hence, radius of smaller circle = 21 cm


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