Question

If the difference between the circumference and the radius of a circle is 37 cm then the circumference of the circle will be​

Answer 1

Given :

The difference between the circumference and the radius of a circle is 37 cm.

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To find :

circumference of the circle.

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Solution :

According to question,

$:\implies\sf 2\pi \: r \: - r = 37$

$:\implies\sf \frac{44}{7} \times r - r = 37$⠀⠀⠀⠀⠀⠀

$:\implies\sf 44 r - 7 r = 37 \times 7$⠀⠀⠀⠀⠀⠀

$:\implies\sf 37r =259$

$:\implies\sf r = 7$⠀⠀⠀⠀⠀

$\therefore\;{\underline{\sf{Radius\;of\;circle\;is\; \bf{7\;cm}.}}}$

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$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 7\ cm}\end{picture}$

We know that,

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$\star\;{\boxed{\sf{\purple{Circumference_{\;(circle)} = 2 \pi r}}}}$

Putting values,

$:\implies\sf 2 \times \dfrac{22}{7} \times 44$

$:\implies{\boxed{\sf{\pink{44\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;circumference \;of\;circle\;is\; \bf{44\;cm}.}}}$

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