The central angle is 60° and arc length is 10π cm.what is the perimeter of the circle?​

1 thought on “The central angle is 60° and arc length is 10π cm.what is the perimeter of the circle?​”

1. Given:-

   • The central angle is 60° and arc length is 10π cm.

   To Find:-

   • Perimeter of the circle

   Formula Used:–

   • [tex]{\boxed{\bf{Length\:of\:Arc=\dfrac{\theta}{360°}\times2\pi r}}}[/tex]

   • [tex]{\boxed{\bf{Circumference\: of \:Circle=2\pi r}}}[/tex]

   Solution:–

   Firstly,

   [tex]\bf :\implies\:Length\:of\:Arc=\dfrac{\theta}{360°}\times2\pi r[/tex]

   [tex]\sf :\implies\:10\pi=\dfrac{60°}{360°}\times2\pi r[/tex]

   [tex]\sf :\implies\:10=\dfrac{1}{6}\times2\times r[/tex]

   [tex]\sf :\implies\:2r=60[/tex]

   [tex]\sf :\implies\:r=\dfrac{60}{2}[/tex]

   [tex]\bf :\implies\:r=30\:cm[/tex]

   Now,

   [tex]\bf :\implies\: Circumference=2\pi r[/tex]

   [tex]\sf :\implies\: Circumference=2\times \dfrac{22}{7}\times 30[/tex]

   [tex]\bf :\implies\: Circumference=\dfrac{132}{7}\:cm[/tex]

   or,

   [tex]\bf :\implies\: Circumference=18.85\:cm[/tex]

   Hence, The Circumference of the given Circle is 132/7cm or 18.85cm.

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