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.

Calculate the arc length to 2 decimal places.

First find what fraction of the whole circle we have.

90° is one quarter of the whole circle (360°).

Therefore, 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.

The formula to calculate the arc length is: \(\text{arc length} = \frac{\text{angle}}{360} \times \pi \times d \)

Question

Calculate the minor arc length to one decimal place.

Calculate the major arc length to one decimal place.