Arc Length, Sector Area and Segments · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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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 radius 6 cm. Find the area of a sector with a central angle of 90 degrees. Leave your answer in terms of pi.

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

  3. True or false: if a sector's central angle is 180 degrees, 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 length, in cm, cut off by a 90 degree angle at the centre. Use pi as 3.14 and round to 1 decimal place.

    Answer: ______________

  5. A circle has radius 5 cm and a sector with a central angle of 90 degrees. Find the segment area, in cm squared. Use pi as 3.14.

    Answer: ______________

  6. A circle has radius 5 cm. A sector has a central angle of 90 degrees. Find the area of the segment, in cm squared. Use pi as 3.14.

    Answer: ______________

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

    • 20 pi cm squared
    • 5 pi cm squared
    • 10 pi cm squared
    • 2.5 pi cm squared

  8. A circle has radius 10 cm. Find the area of a sector with a central angle of 72 degrees. Use pi as 3.14 and give your answer in cm squared.

    Answer: ______________

  9. An arc has a length of 15.7 cm and is cut off by a 90 degree angle at the centre. Using pi as 3.14, find the radius of the circle, in cm.

    Answer: ______________

  10. A circle has radius 8 cm and a sector with a central angle of 90 degrees. Find the segment area, in cm squared. 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. 9 pi cm squared · A quarter of 36 pi is 9 pi.
  3. True · 180 over 360 is a half, for arc and area alike.
  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 · Sector 19.625 minus triangle 12.5 is 7.125.
  7. 10 pi cm squared · 144 over 360 simplifies to 2 over 5, and 2 over 5 of 25 pi is 10 pi.
  8. 62.8 · A fifth of 314 is 62.8.
  9. 10 · A 90 degree angle is a quarter of the full circle, so the full circumference is 4 times 15.7, which is 62.8, and the radius is 62.8 over 6.28.
  10. 18.24 · Sector 50.24 minus triangle 32 is 18.24.
Worksheet · LightMySky