An arc subtends a central angle measuring $$\frac{3 \pi}{2}$$ radians. What fraction of the circumference is this arc? ![](http://admin.getprephub.com/media/editor/ci19_20230216205150305850.png)

An arc subtends a central angle measuring $$(\theta) = \frac{3 \pi}{2}$$ radians Arc length $$({s})={r} \theta=\frac{3 \pi}{2} r$$ Circumference of the circle $$=2 \pi r$$ Required fraction $$=\frac{\text { Arc length }}{\text { Circumference }}=\frac{s}{2 \pi r}=\frac{\frac{3 \pi}{2} r}{2 \pi r}=\frac{3}{4}$$ Arc length= $$\frac{3}{4} \times $$ circumference

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MCQ

An arc subtends a central angle measuring $\frac{3 \pi}{2}$ radians. What fraction of the circumference is this arc?

Select all that apply :

$\frac{3}{4} \text { of the circumference}$

$\frac{1}{4} \text { of the circumference, }$

$\frac{7}{4} \text { of the circumference, }$

$\frac{3}{2} \text { of the circumference, }$

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