2.6 Area of a Part of a Circle

• Parts of a circle: sector, segment, arc, chord
• Length of an arc
• Area of a sector
• Area of a segment
• Applications involving parts of circles

• identify the parts of a circle
• calculate the length of an arc
• calculate the area of a sector
• calculate the area of a segment
• apply these to real life situations

“How do you find the area of a slice rather than the whole circle?”

The titles are open to everyone. Reading a lesson needs an account — sign in or create one.

1. Arcs and sectors
   40 min · 2 practice tasks · quiz
   Taking the right fraction of a circle, and why every formula here is the same idea.
2. Segments and applications
   40 min · 2 practice tasks · quiz
   Subtracting a triangle from a sector, and using it on real curved shapes.
3. Area of an annulus
   40 min · 1 practice tasks · quiz
   The ring between two concentric circles has area pi times (R squared minus r squared).
4. Finding a missing radius of an annulus
   40 min · 1 practice tasks · quiz
   Given the area of a ring and one radius, rearrange pi (R squared minus r squared) to find the other.
5. Minor and major sectors
   40 min · 1 practice tasks · quiz
   Two radii cut a minor sector and a major sector; their angles add to 360 degrees and their areas add to the whole disc.
6. Perimeter of a sector
   40 min · 1 practice tasks · quiz
   The perimeter of a sector is the arc plus two radii, not the arc alone.
7. Finding the angle or radius of a sector
   40 min · 1 practice tasks · quiz
   Rearrange the sector-area and arc-length formulae to find a missing angle or a missing radius.
8. Area of an annular sector
   40 min · 1 practice tasks · quiz
   A slice of a ring - the shape a windscreen wiper sweeps - is the fraction theta/360 of an annulus.
9. The chord and the isosceles triangle
   40 min · 1 practice tasks · quiz
   Two radii and a chord make an isosceles triangle; its area is half r squared sin theta, and the chord is 2 r sin(theta/2).
10. Minor and major segments in depth
    40 min · 1 practice tasks · quiz
    Minor segment is sector minus triangle; major segment is whole minus minor, which is also major sector plus the same triangle.
11. Common region of two intersecting circles
    40 min · 1 practice tasks · quiz
    The lens where two circles overlap is the sum of two segments, one from each circle.
12. Gardens, tracks, dartboards and paths
    40 min · 1 practice tasks · quiz
    Choose annulus, sector, annular sector or segment from a real Kenyan shape, then compute the area that a builder, farmer or designer actually needs.