The area of two circles are in the ratio 9 is to 4 the ratio of their circumference is

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The areas of two circles are in the ratio 4 : 9. What is the ratio between their circumferences ?

The areas of two circles are in the ratio 9 : 4. The ratio of their circumferences is

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)

Concept: Circumference of a Circle

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