Question

The areas of two circles are in the ratio 9 : 4, then what is the ratio of their circumferences?

Answer 1

Given,

`("Area of"  1^(st)  "circle")/("Area of"  2^(nd)  "circle") = 9/4`

i.e., `(≠ r_1^2)/(≠ r_2^2) = 9/4`

⇒ `(r_1^2)/(r_2^2) = 9/4`

Taking the square root of both sides,

`r_1/r_2 = 3/2`

So, `("Circumference of"  1^(st)  "circle")/("Circumference of"  2^(nd)  "circle")`

= `(2 ≠ r_1)/(2 ≠ r_2)`

= `r_1/r_2`

= `3/2`

Hence, the ratio of their circumference is 3 : 2.