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Question
The areas of two circles are in the ratio 9 : 4. The ratio of their circumferences is
Options
3 : 2
4 : 9
2 : 3
81 : 16
Solution
Let the the radii of the two circles be r and R, the circumferences of the circles be c and C and the areas of the two circles be a and A.
Now,
`"a"/"A" = 9/4`
`=>(pi"r"^2)/(pi"R"^2) = (3/2)^2`
`=>"r"/"R" = 3/2`
Now, the ratio between their circumferences is given by
`c/C = (2pi"r")/(2pi"R")`
`="r"/"R"`
`=3/2`
Hence, the correct answer is option (a)
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