Arc Length, Sector Area and Segments · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Arcs, sectors and segments

Mathematics · Geometry · ages 15-16
Name ______________________   Date ____________

  1. A circle has radius 6 cm. Find the area of a 90 degree sector. Leave your answer in terms of pi.

    • 9 pi cm squared
    • 3 pi cm squared
    • 36 pi cm squared

  2. A circle has a radius of 6 cm. Find the area of a sector with a central angle of 90°. Leave your answer in terms of π.

    • 3π cm²
    • 36π cm²
    • 9π cm²
    • 18π cm²

  3. True or false: if a sector's angle is 180°, its arc length is exactly half of the circle's circumference.

    Circle one:   True   False

  4. A circle has radius 12 cm. Find the arc cut off by a 90 degree angle. Use pi as 3.14 and round to 1 decimal place.

    Answer: ______________

  5. A circle has radius 5 cm and a 90 degree sector. Find the segment area. Use pi as 3.14.

    Answer: ______________

  6. A circle has a radius of 5 cm. A sector has a central angle of 90°. Find the area of the segment. Use π = 3.14.

    Answer: ______________

  7. A circle has a radius of 5 cm. What is the area of a sector with a central angle of 144°? Leave your answer in terms of π.

    • 10π cm²
    • 5π cm²
    • 20π cm²
    • 2.5π cm²

  8. A circle has a radius of 10 cm. Find the area of a sector with a central angle of 72°. Use π = 3.14 and give your answer as a decimal.

    Answer: ______________

  9. An arc has a length of 15.7 cm and is cut off by a 90° angle. Using π = 3.14, find the radius of the circle.

    Answer: ______________

  10. A circle has radius 8 cm and a 90 degree sector. Find the segment area. Use pi as 3.14.

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Arcs, sectors and segments W1-mt_z9LIwmfKYJ-s1

  1. 9 pi cm squared · A quarter of 36 pi is 9 pi.
  2. 9π cm² · Sector area works just like arc length: find the fraction of 360° first, then apply it to the whole circle's area.
  3. True · A 180° angle always cuts the circle exactly in half, whether you're measuring arc length or area.
  4. 18.8 · A quarter of the circumference: 75.36 over 4 is 18.84, which rounds to 18.8.
  5. 7.125 · Sector 19.625 minus triangle 12.5 is 7.125.
  6. 7.125 · A 90° sector always makes the triangle part easy: it's just half of radius times radius.
  7. 10π cm² · Simplify the angle fraction first, it makes multiplying by π much easier.
  8. 62.8 · Once you know the fraction of the circle the sector takes up, multiply it by the total area.
  9. 10 · If you know the arc and the angle, scale up to the full circle first, then use the circumference formula to get the radius.
  10. 18.24 · Sector 50.24 minus triangle 32 is 18.24.
Worksheet · LightMySky