Topics
Measurement
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India
Class XI

Areas of Segments (radians)

Lesson
Practice

Interactive practice questions

The diagram shows a circle with radius $8$8 units, and chord $AB$AB subtending an angle of $\frac{\pi}{3}$π3​ radians at the centre.

Find the exact area of the minor segment cut off by chord $AB$AB. Fully simplify your answer.

Easy
5min

The diagram shows a circle with radius $8$8 units, and chord $AB$AB subtending an angle of $\frac{\pi}{3}$π3​ radians at the centre.

Easy
9min

In the diagram, $O$O is the centre of the circle, and sector $OAB$OAB takes up $\frac{4}{9}$49​ of the circle.

Find the area of the minor segment cut off by chord $AB$AB correct to one decimal place.

Easy
6min

The diagram shows a circle with radius $14$14 mm, and chord $AB$AB subtending an angle of $2.3$2.3 radians at the centre.

Find the exact area of the minor segment cut off by chord $AB$AB.

Easy
3min
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Outcomes

11.SF.TF.1

Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Truth of the identity sin^2 x + cos^2 x = 1, for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x + y) and cos (x + y) in terms of sin x, sin y, cos x and cos y. Deducing the identities like following: cot(x + or - y), sin x + sin y, cos x + cos y, sin x - sin y, cos x - cos y (see syllabus document)

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