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प्रश्न
The areas of two circles are in the ratio 4: 9. What is the ratio between their circumferences?
उत्तर
Let 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" = 4/9`
`=> (pi"r"^2)/(pi"R"^2) = (2/3)^2`
`=> "r"/"R" = 2/3`
Now, the ratio between their circumferences is given by
`"c"/"C" = (2pi"r")/(pi"R"^2)`
`= "r"/"R"`
`=2/3`
Hence, the ratio between their circumferences is 2 : 3.
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