5.3 Areas of Sectors and Segments

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A mechanical component for a precision pendulum clock is designed using a triangular metal plate $OAB\,$ attached to a weighted circular sector $OBC\,$ with centre $O$ .

In this design:

$6.5\text{ cm}$
$3.5\text{ cm}$
angle $AOB=π12\displaystyle AOB = \frac{\pi}{12}$ radians
angle $OAB\,$ is an obtuse angle

Determine the size of angle $O A B$ , giving your answer in radians to 4 significant figures.

[3]

Calculate the area of the triangular plate $OAB\,$ in $cm2\text{cm}^2$ , giving your answer to 3 significant figures.

[2]

Given that the ratio of the area of the weighted sector $OBC\,$ to the area of the triangular plate $OAB\,$ is $7:4\,$

Show that angle $BOC\,$ is 0.224 radians to 3 significant figures.

[3]

Hence find the total perimeter of the component, in cm, to the nearest integer.

[3]

5.3 Areas of Sectors and Segments Questions

Practise Edexcel A Level Maths 5.3 Areas of Sectors and Segments with exam-style questions for A Level Maths. 20 questions, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.