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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.
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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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