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Circles

2. Measure the central angle and the Generally, if is a central angle in
length l of the arc. You can measure degree, then the length l of an arc is
the length of the arc by first tracing given by
the arc with a thread and mark πr
l = ____
θ.
the end points. Then, use a ruler 180°
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to measure the length between the For instance, the length of the arc which
marked points. Measure more angles forms a quarter of a circle, subtending
and their corresponding arc lengths. a central angle of 90° (right-angle) is
3. Measure the radius of the circle and given by
find its circumference. Calculate the l = _____
90° πr
l θ 180°
ratio and and compare the
C 360° ___
πr
ratios. = .
2
4. Having the central angle and the Similarly, the arc subtending a central
circumference of the circle, is it angle of 30° has an arc length given by,
possible to find the length of the 30° πr
arc? Give reasons. l = _____
180°
πr
___
5. Formulate the general formula for = .

finding the arc length of a circle. 6
Use the formula you have formed From the formula for finding the arc
to verify the answer you obtained length, the general formula for finding
in task 2. the central angle θ is given by,

6. Share your findings with other 180° l

θ = _____ .
students through a presentation. πr

For instance, the central angle for a
Mathematics for Secondary Schools circumference of a circle is C = 2πr. θ = _____ . Using π = 3.14,
circle of radius r = 2 cm and arc length
From Activity 5.3, you have observed
l = 1 cm is given by,
that the formula for computing the
180° l

This means that, the circumference is
πr
the length of the arc subtending a central
it implies that
angle of 360°.
180° × 1 cm
__________
The length of an arc is proportional to
θ =

3.14 × 2 cm
the measure of its central angle. If the

central angle is 1°, then the length of
the arc can be computed by using the = 28.7°
Therefore, the central angle is 28.7°.
formula
2 rπ
l =
360°
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