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Grade 10 arc length and sector area worksheets

HSG-C.B.5 Measurement and geometry

Printable arc length and sector area worksheets for grade 10, aligned to Common Core standard HSG-C.B.5. A fraction of the whole circle.

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Sample problems

  1. A circle has a radius of 16 cm. What is the length of an arc with a central angle of 90°, in terms of π? 8π cm
  2. A circle has a radius of 9 cm. What is the length of an arc with a central angle of 120°, in terms of π? 6π cm
  3. A circle has a radius of 8 cm. What is the area of a sector with a central angle of 180°, in terms of π? 32π cm²
  4. A circle has a radius of 2 cm. What is the area of a sector with a central angle of 90°, in terms of π? 1π cm²
  5. A circle has a radius of 12 cm. What is the length of an arc with a central angle of 60°, in terms of π? 4π cm
  6. A circle has a radius of 2 cm. What is the length of an arc with a central angle of 180°, in terms of π? 2π cm
  7. A circle has a radius of 8 cm. What is the length of an arc with a central angle of 90°, in terms of π? 4π cm
  8. A circle has a radius of 6 cm. What is the area of a sector with a central angle of 60°, in terms of π? 6π cm²

These eight are one sample at medium difficulty — the generator makes a different set every time.

A worked example

A circle has a radius of 16 cm. What is the length of an arc with a central angle of 90°, in terms of π? 8π cm

  1. 90° is 1/4 of the full 360°
  2. Circumference: 2 × π × 16 = 32π
  3. 1/4 of that: 32 × 1 ÷ 4 = 8, so 8π cm

Every problem on the answer key can show its steps like this — turn on “Show steps” before downloading.

About these worksheets

Each problem states its own measurements, so the reasoning is the same but the arithmetic is new every time. Every sheet is generated fresh, so you can print a new one on the same skill as often as you need — different numbers, same difficulty.

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