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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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