If the circumference of two circles are in the ratio 1 2 what is the ratio of their areas

The ratio of the lengths of the two circles is 5: 2. Find the ratio of a a) the radii of these circles b) the areas for these circles

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

Solution

Let $r_1$ and $r_2$ be the radii of two given circles and $C_1$ and $C_2$ be their circumference.

Then, $C_1:C_2=2:3$

$\Rightarrow 2\pi r_1:2\pi r_2=2:3$

$\Rightarrow r_1:r_2=2:3$

$\Rightarrow r_1^2:r_2^2=4:9$

$\Rightarrow \pi r_1^2:\pi r_2^2=4:9$

Hence, ratio of areas is 4:9.

Mathematics

RD Sharma

Standard X