Sector Area and Arc Length
A sector is a "pizza slice" of a circle. Its arc length and area are calculated as fractions of the full circle, based on the central angle.
What You Need to Know
Key Concept Diagram
Arc length = (theta / 360) x 2 x pi x r, where theta is the central angle in degrees
Sector area = (theta / 360) x pi x r^2
A semicircle is a sector with theta = 180 degrees
The full circle corresponds to theta = 360 degrees
Key Vocabulary
Sector
A region bounded by two radii and the arc between them; a "pizza slice"
Arc
The curved edge of a sector, part of the circle's circumference
Central angle
The angle at the centre of the circle that defines the sector
Radius
The distance from the centre of the circle to its edge
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
Find the arc length of a sector with radius 6 cm and central angle 90 degrees. (Use pi = 3.14)
Question 2
What is the area of a sector with radius 10 cm and central angle 120 degrees? (Use pi = 3.14)
Question 3
A sector has an area of 25.12 cm^2 and radius 4 cm. What is the central angle? (Use pi = 3.14)
Key Concepts Summary
- ●Arc length = (theta / 360) x 2 x pi x r, where theta is the central angle in degrees
- ●Sector area = (theta / 360) x pi x r^2
- ●A semicircle is a sector with theta = 180 degrees
- ●The full circle corresponds to theta = 360 degrees