Question

Two circles touches internally having circumferences 352 cm and 396 cm, then difference between their radii is
a)14cm b)7cm c)21cm d)28cm​

Answer 1

$\underline{\textbf{Given:}}$

$\textsf{Two circles  touches internally having circumferences}$

$\textsf{352 cm and 396 cm}$

$\underline{\textbf{To find:}}$

$\textsf{Difference between their radii}$

$\underline{\textbf{Solution:}}$

$\mathsf{Let\;the\;radii\;of\;two\;circles\;be\;r_1\;and\;r_2\;with\;r_1\;>\;r_2}$

$\textsf{As per given data,}$

$\mathsf{2\,\pi\,r_1=396\;\;\;\&\;\;\;2\,\pi\,r_2=352}$

$\mathsf{\pi\,r_1=198\;\;\;\&\;\;\;\pi\,r_2=176}$

$\mathsf{r_1=\dfrac{198}{\pi}\;\;\;\&\;\;\;r_2=\dfrac{176}{\pi}}$

$\mathsf{Now,}$

$\mathsf{r_1-r_2}$

$\mathsf{=\dfrac{198}{\pi}-\dfrac{176}{\pi}}$

$\mathsf{=\dfrac{198-176}{\pi}}$

$\mathsf{=\dfrac{22}{\pi}}$

$\mathsf{=\dfrac{22}{\dfrac{22}{7}}}$

$\mathsf{=22{\times}\dfrac{7}{22}}$

$\mathsf{=7\;cm}$

$\underline{\textbf{Answer:}}$

$\mathsf{Option\;(b)\;is\;correct}$