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