AI generatedGeometry and measuresKS3 / GCSE

Sector angle from its area

Sector angle from its area.

  • A sector uses the fraction of the whole circle.
  • Arc length comes from circumference; sector area comes from circle area.
  • Perimeter includes straight edges too. An annulus is outer-circle area minus inner-circle area.

Example 1

A sector has radius 3 cm and area . Find its angle.

Circle geometry, not to scaleNot to scale
Compare the sector measurement with the corresponding whole-circle measurement.Use the same fraction of a full turn.

Example 2

A sector has radius 4 cm and area . Find its angle.

Circle geometry, not to scaleNot to scale
Compare the sector measurement with the corresponding whole-circle measurement.Use the same fraction of a full turn.

Your turn

Question 1

A sector has radius 5 cm and area . Find its angle.

Circle geometry, not to scaleNot to scale
Check answer
Compare the sector measurement with the corresponding whole-circle measurement.Use the same fraction of a full turn.
Question 2

A sector has radius 6 cm and area . Find its angle.

Circle geometry, not to scaleNot to scale
Check answer
Compare the sector measurement with the corresponding whole-circle measurement.Use the same fraction of a full turn.
Question 3

A sector has radius 7 cm and area . Find its angle.

Circle geometry, not to scaleNot to scale
Check answer
Compare the sector measurement with the corresponding whole-circle measurement.Use the same fraction of a full turn.
Question 4

A sector has radius 8 cm and area . Find its angle.

Circle geometry, not to scaleNot to scale
Check answer
Compare the sector measurement with the corresponding whole-circle measurement.Use the same fraction of a full turn.
Question 5

A sector has radius 9 cm and area . Find its angle.

Circle geometry, not to scaleNot to scale
Check answer
Compare the sector measurement with the corresponding whole-circle measurement.Use the same fraction of a full turn.
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