Question

If the circumference to two circles are in ratio 2:3.find the ratio of their area.

Answer 1

Heya!!!

This is the answer of your query.

it is given that the ratio between the circumference is 2:3.

We know that circumference of circle is 2πr and area is πr².

$ratio \: of \: circumference \: = \frac{2\pi \times r1}{2\pi \times r2} = \frac{2}{3} \\ - > \frac{r1}{r2} = \frac{2 }{3}$

Therefore,
$ratio \: of \: areas \: of \: circles = \frac{\pi \times {r1}^{2} }{\pi \times {r2}^{2} } = \frac{4}{9}$
Hence, the ratio between areas of two circle will be 4/9.

Hope you got the answer

Answer 2

Given: Ratio of circumference of two circles = 2 : 3

2πr/2πr=2/3

r/R=2/3

(r/R)^2 =(2/3)^2

r^2/R^2=2^2/3^2

4/9

Now ratio of area of two circles = πr2 : πR2 
Hence the required ratio is 4 : 9