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