Mathematics·Mensuration · NSSCO 4.2
The circle: circumference, area, arcs & sectors
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The circle turns up everywhere, and this lesson makes every circle question feel calm and doable. We name all the parts — centre, radius, diameter, chord, arc, sector, segment and tangent — then meet the special number pi. We use it to find the circumference (the distance around) and the area (the space inside), learn to work the formulas backwards, and then handle arcs, sectors, their perimeters and semicircles. We finish with compound shapes and real money problems in Namibian dollars.
What you'll learn in this lesson
By the end you should be able to (NSSCO Mathematics 4.2):
- Name and identify the parts of a circle: centre, radius, diameter, chord, arc, sector, segment and tangent
- Understand pi as the ratio of circumference to diameter and use C = pi d = 2 pi r for the circumference
- Use A = pi r squared for the area of a circle, and work both formulas backwards to find a radius or diameter
- Find the arc length as the fraction (theta over 360) of the circumference, and the sector area as the same fraction of the area
- Find the perimeter of a sector (arc + 2 radii) and work with semicircles
- Solve problems involving compound shapes made from circles and semicircles, including cost problems in Namibian dollars
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