Curriculum placement
Geometry. This describes the skill, not a learner estimate.
Arc length and sector area
Calculate arc length and sector area
Problem types
- Arc length, radians and sector area from proportion
- Arc length
- Sector area
- Arc length from a central angle, rounded
Builds on
- Circumference and area of a circle
- Percent of a number
- Multiplying fractions
- Measuring angles
- Why every circle is similar to every other · Earlier idea
Because circles are similar, arc length and sector area are fixed fractions of circumference and area, scaling with the radius.
- Fractions of an area · Earlier idea
Dividing a region into equal-area parts extends to a sector that is a fraction of a whole circle.
- Halves, thirds, and quarters · Earlier idea
Equal parts of a circle are sectors, and a sector is a fraction of the whole circle.
Leads to
- Radians and the unit circle
- Modeling with geometry · See it applied
Sector and arc measures model curved shapes such as a pie slice or a curved fence.
- Area from two sides and the included angle · See it applied
The area of a circular segment is the sector area minus the triangle area, which combines sector and trigonometric area.
Related skills
- Volume of cylinders, cones, and spheres · Shared foundations
- Why the circle and solid formulas hold · Shared foundations
- The multiplication rule for probability · Shared foundations
- Two-way tables · Shared foundations
Open the interactive map to explore lessons and skill connections.