Question

The areas of two concentric circles are 962.5 cm² and 1386 cm² respectively. Find the width of the ring.​

Answer 1

⧠ Let r be the inner radius and R be the outer radius of the ring.

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$:\implies\sf{Area_{(inner\;circle)}=πr^2}\\\\\\:\implies\sf{962.5=\dfrac{22}{7}×r^2}\\\\\\:\implies\sf{r^2=\dfrac{962.5×7}{22}}\\\\\\:\implies\sf{r^2=306.25}\\\\\\:\implies\sf{r^2=(17.5)^2}\\\\\\:\implies{\underline{\boxed{\frak{r=17.5\;cm}}}}{\;\bigstar}$

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And,

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$:\implies\sf{Area_{(outer\;circle)}=πR^2}\\\\\\:\implies\sf{1386=\dfrac{22}{7}×R^2}\\\\\\:\implies\sf{R^2=\dfrac{1386×7}{22}}\\\\\\:\implies\sf{R^2=441}\\\\\\:\implies\sf{R^2=(21)^2}\\\\\\:\implies{\underline{\boxed{\frak{R=21\;cm}}}}{\;\bigstar}$

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Now,

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$:\implies\sf{Width\;of\;the\;ring=R-r}\\\\\\:\implies\sf{Width\;of\;the\;ring=(21-17.5)\;cm}\\\\\\:\implies{\underline{\boxed{\blue{\frak{Width\;of\;the\;ring=3.5\;cm}}}}}{\;\bigstar}$

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$\therefore{\underline{\sf{The\;width\;of\;the\;ring\;is\;{\bf{3.5\;cm}}.}}}$