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Question
The radii of two circles are in the ratio 3: 8. If the difference between their areas is 2695π cm2, find the area of the smaller circle.
Solution
Let the radius of the two circles be 3r and 8r respectively.
area of the circle having radius 3r = π(3r)2
= 9πr2
area of the circle having radius 8r = π(8r)2
= 64πr2
According to the question
64πr2 - 9πr2 = 2695π
55r2 = 2695
r2 = 49
r = 7 cm
Hence the radius of the smaller circle is 3 x 7 = 21 cm
Area of the smaller circle is given by
A = πr2 =`22/7 xx 21^2 = 1386 "cm"^2`
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