Question

What is the angle subtended at the centre of a circle of radius 6 cm by an arc of length 6 pie cm.​

Answer 1

Given: The radius of circle is 6 cm and length of arc is 6 π cm.

Need to find: The angle subtended at the centre of circle.

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» To find the angle subtended of the given circle, we can use Length of the arc formula that is Given by :

$\qquad\qquad\qquad\bigstar\underline{\boxed{\pmb{\frak{{Length}_{(arc)}=\dfrac{\theta}{360}\times 2\pi r}}}}$

where:

• r is radius of the circle.
• Length of arc is 6π cm and given radius is 6cm.

⠀

$\begin{gathered}\underline{\bf{\dag} \:\mathfrak{Substituting\;values\;in\; formula\: :}}\\\\\end{gathered}$

$\qquad:\implies\sf{6\pi=\dfrac{\theta}{360}\times 2\times \pi\times 6}$

$\\\qquad:\implies\sf{6\pi=\dfrac{\theta}{180}\times \pi\times 6}$

$\\\qquad:\implies\sf{6\pi=\dfrac{\theta}{30}\times \pi}$

$\\\qquad\quad:\implies\sf{6=\dfrac{\theta}{30}}$

$\\\qquad\quad:\implies\sf{\theta=6\times 30}$

$\\\qquad\quad:\implies\underline{\boxed{\pmb{\frak{\color{blue}{\theta=180}}}}}\: \bigstar$

$\\\therefore\underline{\sf{Hence,\: the\; angle\: subtended\: at\: the\: center\: of\: circle\: is\:}\bold{{180}^{\circ}}}$