Question

The areas of two circles are in the ratio 49 : 64. Find the ratio of their circumferences.

Answer 1

Given, the area of two circles are in the ratio 49 : 64

Area of a circle = πr²

Let area of the first circle = `pir_1^2`

And area of the second circle = `pir_2^2`

According to the question,

`49/64 = (pir_1^2)/(pir_2^2)`

⇒ `49/64 = r_1^2/r_2^2`

⇒ `(7)^2/(8)^2 = r_1^2/r_2^2`

⇒ `(7/8)^2 = (r_1/r_2)^2`

∴ r₁ = 7 and r₂ = 8

The ratio of circumferences of these two circles

= `(2pir_1)/(2pir_2)`   ...[∵ Circumference of circle = 2πr]

= `r_1/r_2`

= `7/8`   

Hence, required ratio is 7 : 8