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