Question

The circumferences of two circles are in the ratio 2: 3. What is the ratio between their areas?

Answer 1

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.