Question

An arc subtends a central angle measuring 2pi/3

Answer 1

Answer:

1/3

Step-by-step explanation:

We know that angle subtended by whole circumference is $2\pi$.

If r is the radius then Length of whole circumference is $2\pi r$

$2\pi$ radian has $2\pi r$  length

dividing  both side by $2\pi$ we have

$2\pi /2\pi = 2\pi r/2\pi \ circumference$

1 radian has r length  

1 radian = r length      equation a

=> since we have to find value of circumference for $2\pi /3$ we

multiply both side of equation a with $2\pi /3$.

$2\pi /3 \radian = r* 2\pi /3 \circumference$

therefore, length of required arc is $2\pi r/3$

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we have to find how much is this as fraction of total  circumference of circle

fraction of circumference = value of arc length / total length of circumference

fraction of circumference = $=>(2\pi r/3) / 2\pi r\\=> 1/3$

Thus, the given arc is 1/3 of circumference of circle.