Arc length
A chord separates the circumference of a circle into two sections - the major arc and the minor arc.
It also separates the circle into two segments - the major segment and the minor segment.
The formula to calculate the arc length is: \(\text{Arc length} = \frac{\text{angle}}{360^\circ} \times \pi \text{d}\)
Example
Calculate the arc length to 2 decimal places.
First calculate what fraction of a full turn the angle is.
90掳 is one quarter of a full turn (360掳).
The arc length is \(\frac{1}{4}\) of the full circumference.
Remember the circumference of a circle = \(\pi d\) and the diameter = \(2 \times \text{radius}\).
The arc length is \(\frac{1}{4} \times \pi \times 8 = 2 \pi\). Rounded to 3 significant figures the arc length is 6.28cm.
Question
Calculate the minor arc length to one decimal place.
\(\text{Arc length} = \frac{144^\circ}{360^\circ} \times \pi \times 7 = 8.8~\text{cm}\)
Question
Calculate the major arc length to one decimal place.
The major sector has an angle of \(360^\circ - 110^\circ = 250^\circ\).
\(\text{Arc length} = \frac{250^\circ}{360^\circ} \times \pi \times 12 = 26.2~\text{cm}\)