Q. 144.3( 3 Votes )

# The difference be

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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