M4.4.7 For the adult
Arcs and sectors
A quarter of a round flat bread has a radius of 10 cm. How long is its curved edge?
What this chapter teaches
A sector with an angle θ at the centre is θ ÷ 360 of the whole circle. Its arc length is that fraction of 2πr and its area is that fraction of πr². The perimeter of a sector is the arc length plus two radii.
Three questions to ask
There is no one right wording. Listen for the idea.
- What fraction of a circle is a sector with an angle of 90°, and what is its arc length for a radius of 10 cm?
- Why does the perimeter of a sector need two radii as well as the arc?
- How is finding an arc length different from finding a sector area?
After the chapter, the learner can
- Find the length of an arc of a circle
- Find the area of a sector
- Find the perimeter of a sector
What they copy into their notebook
Arc = (θ ÷ 360) × 2πr. Sector area = (θ ÷ 360) × πr². Sector perimeter = arc + 2r. Say how you rounded.