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Question
The areas of two circles are in the ratio 49 : 64. Find the ratio of their circumferences.
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Solution
Given, the area of two circles are in the ratio 49 : 64
Area of a circle = πr2
Let area of the first circle = `pir_1^2`
And area of the second circle = `pir_2^2`
According to the question,
`49/64 = (pir_1^2)/(pir_2^2)`
⇒ `49/64 = r_1^2/r_2^2`
⇒ `(7)^2/(8)^2 = r_1^2/r_2^2`
⇒ `(7/8)^2 = (r_1/r_2)^2`
∴ r1 = 7 and r2 = 8
The ratio of circumferences of these two circles
= `(2pir_1)/(2pir_2)` ...[∵ Circumference of circle = 2πr]
= `r_1/r_2`
= `7/8`
Hence, required ratio is 7 : 8
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