Determine the angle (in radians) subtended at the centre of a circle of radius $$3$$ cm by each of the following arcs:

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Uniteasy Admin · Accepted Answer

The arc length can be expressed in terms of centered angle in degrees or radians 
$$l =\dfrac{n\pi r}{180\degree }  = r	heta $$
In this question, the angle is required in radians. So the arc length formula to be used is 
$$l   = r	heta =3	heta  $$
 ($$r =3$$ cm)arc of length $$6$$ cm
$$l = 6$$ cm
then
$$6 = 3	heta $$
$$	heta =2 $$ arc of length $$3π $$   cm
l = $$3π $$   cm
$$3π = 3	heta  $$
$$	heta =\pi   $$ arc of length $$1.5$$ cm
$$l = 1.5$$ cm
$$1.5 = 3	heta $$
$$	heta =0.5 $$ arc of length $$6π $$ cm
$$l = 6π $$ cm
$$6π =3	heta  $$
$$	heta  =2\pi  $$

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