Arc Length & Sector Area Worksheet
Goal: Find arc lengths, sector areas and chords, connect degrees to radians, and see how each measurement changes with the angle and the radius.
What to do
- Open the arc length & sectors tool and set “Radius” to 5.
- For each central angle in the table, press its button (or type it into “Central angle (°)”) and record the arc length, sector area, chord length and fraction of the circle.
- Set “Radius” to 10 and “Central angle (°)” to 90, and record the last row.
Record your results
| Setting | Arc length | Sector area | Chord length | Fraction of circle |
|---|---|---|---|---|
| r = 5, θ = 30° | ||||
| r = 5, θ = 60° | ||||
| r = 5, θ = 90° | ||||
| r = 5, θ = 180° | ||||
| r = 5, θ = 270° | ||||
| r = 10, θ = 90° |
Questions
Convert 60° to radians, then use s = rθ to find the arc length by hand.
Compare the 90° sector of radius 5 with the 90° sector of radius 10. What happened to the arc length and the sector area when the radius doubled?
Explain why the chord for 60° is exactly 5, the same as the radius.
Why is the chord for 180° equal to 10? Why is the chord for 270° the same as the chord for 90°?
An arc on a circle of radius 5 is 10 units long. Find the central angle in radians and in degrees.
Show that the degree formula A = (θ ÷ 360) × πr² gives the same sector area as A = ½r²θ for a 90° sector of radius 5.
Free from Geometry Lab · geometrylab.net · HSG-C.B.5: Show that arc length is proportional to the radius, define radian measure, and derive the formula for the area of a sector.
Teaching with this? Find the answer key and more activities on the Geometry Lab for teachers page.