The circumference of two circles are in the ratio 2 : 3 the ratio of their areas is

Let’s assume the radius of two circles ${{C}_{1}}$ and ${{C}_{2}}$ be ${{r}_{1}}$ and ${{r}_{2}}$

We all know that, Circumference of a circle (C) $=2\pi r$

And their circumference will be $2\pi {{r}_{1}}$ and $2\pi {{r}_{2}}$.

Then, their ratio is $={{r}_{1}}:{{r}_{2}}$

Given in the question, circumference of two circles is in a ratio of $2:3$

${{r}_{1}}:{{r}_{2}}=2:3$

Now, the ratios of their areas is given as

$=\pi r_{1}^{2}:\pi r_{2}^{2}$

$={{\left( \frac{r1}{r2} \right)}^{2}}$

$={{\left( \frac{2}{3} \right)}^{2}}$

$=\frac{9}{16}$

$=\frac{4}{9}$

Thus, ratio of their areas $=4:9$.

The circumference of two circles are in ratio 2:3. Find the ratio of their areas

Let radius of two circles be 𝑟1 and 𝑟2 then their circumferences will be 2𝜋𝑟1 : 2𝜋𝑟2
= 𝑟1: 𝑟2

But circumference ratio is given as 2 : 3

𝑟1: 𝑟2 = 2: 3

Ratio of areas = 𝜋𝑟22: 𝜋𝑟22

`= (r_1/r_2)^2`

`=(12/3)^2`

`= 4/9`

= 4:9

∴ 𝑟𝑎𝑡𝑖𝑜 𝑜𝑓 𝑎𝑟𝑒𝑎𝑠 = 4 ∶ 9

Concept: Circumference of a Circle

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The circumference of two circles are in the ratio 2 : 3. Find the ratio of their areas.