JAMB 2003 · UME · Q32

Plane mensuration

An arc of a circle subtends an angle of $30^\circ$ at the circumference of a circle of radius 21 cm. Find the length of the arc. $\left[\pi = \frac{22}{7}\right]$

Worked solution (try it first)

The angle at the centre is twice the angle at the circumference, so the arc subtends $60^\circ$ at the centre.
The circumference is $2 \times \frac{22}{7} \times 21 = 132$ cm.
The arc is $\frac{60}{360} = \frac16$ of it: $132 \div 6 = 22$ cm, option C.

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