A circle's center is at $(3 ,1 )$ and it passes through $(0 ,2 )$ . What is the length of an arc covering $( pi ) /6$ radians on the circle?

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Answer 1 · 2016-10-24T16:25:45

$(pisqrt10)/6units$

the arc length of is calculated using $color(blue)(s=rtheta)$

where $r$ is the radius of the circle

& $theta$ is the angle subtended by the arc at the centre of the circle.

1) Find the radius of the circle, this is done by Pythagoras

$r=sqrt((3-0)^2+(1-2)^2$

$r=sqrt(9+1)=sqrt10$

2) arc length

$s=rtheta=sqrt10xxpi/6$

$:.s=(pisqrt10)/6 units$

A circle's center is at (3 ,1 )(3 ,1 ) and it passes through (0 ,2 )(0 ,2 ). What is the length of an arc covering ( pi ) /6 ( pi ) /6 radians on the circle?