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Worksheets›Geometry›Circles›Arc length and sector area

Arc Length and Sector Area Worksheets

Free printable worksheets with answer keys. Pick a level, preview the questions, then open the sheet to swap or delete any single question.

GeometryCCSS HSG.C.B.5Answer key includedPDF · Print
Open in generatorStart with an easy sheet

Easy: Arc length

  1. 1.Find the length of the arc of the shaded sector.6 cm150°
  2. 2.Find the length of the arc of the shaded sector.15 cm30°
  3. 3.Find the length of the arc of the shaded sector.2 cm72°
  4. 4.Find the length of the arc of the shaded sector.10 cm72°
  5. 5.Find the length of the arc of the shaded sector.16 cm45°
  6. 6.Find the length of the arc of the shaded sector.6 cm80°
Preview shows 6 of 12 questions. Every sheet is new; open it to change any question.

Worksheet variations

A sector with a central angle of θ° is θ/360 of the whole circle. Its arc is that fraction of the circumference: (θ/360) × 2πr. Its area is that fraction of the circle's area: (θ/360) × πr². Simplify the fraction before multiplying and leave π in the answer.

EasyFind the length of the arc of the shaded sector.13 cm300°Arc lengthMediumFind the area of the shaded sector.13 cm40°Sector areaHardThe arc of the shaded sector is 163π cm long. Find the central angle x.4 cmx°The central angle from the arc

How to solve it: a worked example

Give exact answers in terms of π.

  1. StartFind the length of the arc of the shaded sector.17 cm60°
  2. The sector's share of the circle60360 = 16
  3. Multiply by the circumference16 × 2π(17) = 173π
  4. Answer173π cm

Common mistakes to watch for

  • Using the diameter where the formula needs the radius.
  • Using πr² for an arc length, or 2πr for a sector area.
  • Dividing by 180 instead of 360.

Tip: tick “Step-by-step answer key” in the generator to print each step for marking.

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FAQ

How are arc length and sector area alike?

Both are a fraction of the whole circle: the central angle over 360°. Arc length = (θ/360) × 2πr and sector area = (θ/360) × πr².

What if the angle is given in radians?

The formulas get simpler: arc length = rθ and sector area = ½r²θ, with θ in radians.

Is every worksheet different?

Yes. Numbers are generated each time, and the answer key is calculated for that sheet. Swap any single question and its answer updates too.

Can I mix arc length and sector area with other skills?

Yes. In the generator, add more skills; each gets its own section on the sheet with its own instructions.

Is it free to print?

Yes. Generating and printing from the browser is free with no sign-up. PDF downloads need a free account.