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Question
The radii of two circles are in the ratio 5 : 8. If the difference between their areas is 156p cm2, find the area of the bigger circle.
Solution
Let r1 and r2 be the radii of two circles.
⇒ r1 : r2 = 5:8
⇒`"r"_1/"r"_2 = (5)/(8)`
⇒ r1 = `(5)/(8)"r"_2`
It is given that,
πr22 - πr12 = 156π
⇒ r22 - r12 = 156
⇒ `"r"_2^2 - (5/8"r"_1)^2` = 156
⇒ `"r"_2^2 - (25)/(64)"r"_2^2` = 156
⇒ `(64"r"_2^2 - 25"r"_2^2)/(64)` = 156
⇒ 39r22 = 64 x 156
⇒ r22 = `(64 xx 156)/(39)` = 256
⇒ r2 = 16
∴ Area of bigger circle
= πr22
= `(22)/(7) xx 16 xx 16`
= 804.57cm2.
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