5.3 Areas of Sectors and Segments

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A designer is drafting a logo for a renewable energy company. The design features a central polished circular sector $O B C$ , with centre $O$ , flanked by two identical triangular 'rays', $O A B$ and $O D C$ . The points $A, O,$ and $D$ lie on a straight horizontal line. The vertices $B$ and $C$ lie on the circular arc that forms the boundary of the sector.

Given that:

angle $B O C = 1.8$ radians
the area of sector $\text{ cm}^2$
$A O D$ is a straight line segment with a total length of $\text{ cm}$

Determine the radius of the circular sector, giving your answer in $cm\text{cm}$ to 2 decimal places.

[3]

Calculate the size of angle $A O B$ in radians, giving your answer to 2 decimal places.

[2]

Hence find: the total area of the logo, giving your answer in $cm2\text{cm}^2$ to one decimal place.

[3]

the total perimeter of the logo, giving your answer in $cm\text{cm}$ to one decimal place.

[4]

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.