Question

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

Answer 1

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.