The circumference of a circle is 60 cm. what is the length of an arc of140 degree?

Question:

The circumference of a circle is 60 cm. what is the length of an arc of {eq}140^o {/eq}?

Circumference of the Circle:

Circumference of the circle is defined as the linear length of the circle. The circumference is also known as the special case of the perimeter. The formula to calculate the circumference of the circle is as follows,

{eq}C = 2\pi r {/eq}

Here, the radius of circle is {eq}r {/eq}.

Answer and Explanation:


Given Data

  • The circumference is: {eq}C = 60\;{\rm{cm}} {/eq}
  • The angle is: {eq}\theta = 140^\circ {/eq}


The expression for the circumference of a circle is,

{eq}C = 2\pi r {/eq}


Here, the radius of the circle is {eq}r {/eq}.


The length of an arc of a circle is,

{eq}\begin{align*} L &= \dfrac{\theta }{{360^\circ }}\left( {2\pi r} \right)\\ &= \dfrac{\theta }{{360^\circ }}\left( C \right) \end{align*} {/eq}


Substitute the known value of circumference,

{eq}\begin{align*} L &= \dfrac{{140^\circ }}{{360^\circ }}\left( {60\;{\rm{cm}}} \right)\\ &= 23.333\;{\rm{cm}} \end{align*} {/eq}


Thus, the length of an arc is {eq}23.333\;{\rm{cm}} {/eq}.


Learn more about this topic:

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Diameter and Circumference Related with Pi

from Remedial Algebra I

Chapter 25 / Lesson 4
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