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# The circumferences of the two concentric circles are $12\ cm$ and $72\ cm$. What is the difference between their radii?

**Given: **The circumferences of the two concentric circles are $12\ cm$ and $72\ cm$.

**To do: **To find the difference between their radii.

**Solution:**

Let $r_1$ and $r_2$ be the radii of the concentric circles.

$therefore$ circumference of the given circles are $2\pi r_1$ and $2\pi r_2$.

$\therefore 2\pi r_1=12$ and $2\pi r_2=72$

$\Rightarrow 2\pi r_2-2\pi r_1=72-12=60$

$\Rightarrow 2\pi( r_2-r_1)=60$

$\Rightarrow r_2-r_1=\frac{60}{2\pi}$

$\Rightarrow r_2-r_1=\frac{30}{\pi}$

$\Rightarrow r_2-r_1=\frac{30}{\frac{22}{7}}$

$\Rightarrow r_2-r_1=9.55$

$\therefore$ The difference between radii of the given concentric circles is $9.55$.

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