Q14 of 47 Page 1

The difference between the radii of the smaller circle and the larger circle is 7 cm and the difference between the areas of the two circles is 1078 sq.cm. Find the radius of the smaller circle.

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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