Question

Annyeong!!

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Answer 1

Given:-

• Circumference of 2 circles is 2:3

To find:-

• Ratio of area of both circles

Solution:-

Let's assume ratio of circumference be 2x:3x

Then,

$\sf \dfrac {Circumference\;of\:1st\:circle}{Circumference\:of\:2nd\: circle}=\dfrac {2x}{3x}$

Applying formula for circumference of circle=2πr.

$\sf \dfrac {2\pi r_1}{2\pi r_2}=\dfrac {2x}{3x}$

2π will be cancelled

$\boxed{\sf \dfrac { r_1}{r_2}=\dfrac {2x}{3x}}$

This is the ratio of radius of circles.

$\rule {200}{1}$

Now applying formula for area.

$\sf \dfrac{Area\:of\: circle_1}{Area\:of\: circle_2}=\dfrac{\pi r_1^2}{\pi r_2^2}$

π will be cancelled and substitute ratio of radius.

$\sf \dfrac{Area\:of\: circle_1}{Area\:of\: circle_2}=\bigg(\dfrac{2x}{3x}\bigg)^2$

$\sf \dfrac{Area\:of\: circle_1}{Area\:of\: circle_2}=\dfrac{4x^2}{9x^2}$

Cancel x² from Nr. And Dn.

$\sf \dfrac{Area\:of\: circle_1}{Area\:of\: circle_2}=\dfrac{4}{9}$

So the required ratio of area of circle is 4:9.