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 $\frac{π}{6}$ $( pi ) /6$ radians on the circle?

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Answer 1 · 2016-10-24T16:25:45

$\frac{π \sqrt{10}}{6} u n i t s$ $(pisqrt10)/6units$

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

where $r$ $r$ is the radius of the circle

& $θ$ $theta$ 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

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

$r = \sqrt{9 + 1} = \sqrt{10}$ $r=sqrt(9+1)=sqrt10$

2) arc length

$s = r θ = \sqrt{10} \times \frac{π}{6}$ $s=rtheta=sqrt10xxpi/6$

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

A circle's center is at (3 ,1 )(3,1)(3 ,1 ) and it passes through (0 ,2 )(0,2)(0 ,2 ). What is the length of an arc covering ( pi ) /6 π6( pi ) /6 radians on the circle?