Question

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

arc of length 6 cm

arc of length cm

arc of length 1.5 cm

arc of length cm

Collected in the board: Circles problems

Steven Zheng posted 13 minutes ago

Answer

The arc length can be expressed in terms of centered angle in degrees or radians

l =\dfrac{n\pi r}{180\degree } = r\theta

In this question, the angle is required in radians. So the arc length formula to be used is

l = r\theta =3\theta

(r =3 cm)

arc of length 6 cm

l = 6 cm

then

6 = 3\theta

\theta =2

arc of length cm

l = cm

3π = 3\theta

\theta =\pi

arc of length 1.5 cm

l = 1.5 cm

1.5 = 3\theta

\theta =0.5

arc of length cm

l = 6π cm

6π =3\theta

\theta =2\pi

Steven Zheng posted 1 minute ago

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