Question

If the circumference of two circles are in the ratio  2 : 3, what is the ratio of their areas?

Answer 1

We are given ratio of circumferences of two circles. If `C=2 pir` and `C'=2pi r'` are circumferences of two circles such that 

`C/C'=2/3`

⇒` (2pi r)/(2pi r')=2/3` ..............(1) 

Simplifying equation (1) we get,

`r/(r')=2/3`

Let `A=pir^2` and `A'=pir^('2)` are the areas of the respective circles and we are asked to find their ratio.

`A/A'=(pir^2)/(pir^('2))`

`A/A'=r^2/r^('2)`

`A/A'=(r/(r'))^2`       ...................(2)

We know that `r/(r')=2/3`substituting this value in equation (2) we get,

`A/(A')=(2/3)^2`

`⇒ A/(A')=4/9`

Therefore, ratio of their areas is `4:9`