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 $=4:9$.
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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
Is there an error in this question or solution?