Work through in order — each question is a small step harder than the last. Show your working. Give each answer to 3 significant figures.

1. 1The diagram shows a sector of a circle with radius $14$ cm and angle $72^\circ$ at the centre.
   Work out the length of the arc of the sector.
2. 2The diagram shows a sector of a circle with radius $14$ cm and angle $300^\circ$ at the centre.
   Work out the length of the arc of the sector.
3. 3The diagram shows a sector of a circle with radius $9$ cm and angle $300^\circ$ at the centre.
   Work out the length of the arc of the sector.
4. 4The diagram shows a sector of a circle with radius $5$ cm and angle $120^\circ$ at the centre.
   Work out the area of the sector.
5. 5The diagram shows a sector of a circle with radius $14$ cm and angle $300^\circ$ at the centre.
   Work out the area of the sector.
6. 6The diagram shows a sector of a circle with radius $17$ cm and angle $36^\circ$ at the centre.
   Work out the perimeter of the sector.
7. 7The diagram shows a sector of a circle with radius $6$ cm and angle $300^\circ$ at the centre.
   Work out the perimeter of the sector.
8. 8A sector of a circle has an angle of $18^\circ$ at the centre.
   What percentage of the area of a semicircle of the same radius is the area of this sector?
9. 9A sector of a circle has an angle of $36^\circ$ at the centre.
   What percentage of the area of a semicircle of the same radius is the area of this sector?
10. 10A sector of a circle has radius $5$ cm.
    The length of its arc is $20.9$ cm.
    Work out the area of the sector.
11. 11A sector of a circle has radius $10$ cm.
    The length of its arc is $55$ cm.
    Work out the area of the sector.
12. 12A running track is made of two straight sections, each of length $94$ m, and two semicircular ends, each of radius $39$ m.
    A runner wants to run at least $3828$ m.
    What is the smallest number of complete laps they must run?
13. 13A running track is made of two straight sections, each of length $86$ m, and two semicircular ends, each of radius $31$ m.
    A runner wants to run at least $1617$ m.
    What is the smallest number of complete laps they must run?
14. 14A cyclist rides once around a track made of two straight sections, each of length $92$ m, and two semicircular ends, each of radius $27$ m.
    The lap takes $61$ seconds.
    Work out the cyclist’s average speed in m/s.
15. 15A cyclist rides once around a track made of two straight sections, each of length $113$ m, and two semicircular ends, each of radius $38$ m.
    The lap takes $42$ seconds.
    Work out the cyclist’s average speed in m/s.
16. 16The diagram shows a sector of a circle with radius $12$ cm.
    The area of the sector is $60\pi$ cm².
    Work out the angle $x$ of the sector.
    Give your answer in degrees.
17. 17The diagram shows a sector of a circle with radius $15$ cm.
    The area of the sector is $25\pi$ cm².
    Work out the angle $x$ of the sector.
    Give your answer in degrees.
18. 18The diagram shows a sector of a circle with radius $6$ cm.
    The perimeter of the sector is $16.2$ cm.
    Work out the angle $x$ of the sector.
19. 19The diagram shows a sector of a circle with radius $6$ cm.
    The perimeter of the sector is $16.7$ cm.
    Work out the angle $x$ of the sector.
20. 20A sector of a circle has angle $45^\circ$ at the centre.
    The length of its arc is $10.2$ cm.
    Work out the radius of the sector.
21. 21A sector of a circle has angle $120^\circ$ at the centre.
    The length of its arc is $12.6$ cm.
    Work out the radius of the sector.
22. 22The diagram shows a sector $OAB$ of a circle, centre $O$, with $OA = OB = 7$ cm and angle $AOB = 130^\circ$. $AB$ is a chord.
    Work out the area of the shaded segment (between the chord $AB$ and the arc).
23. 23The diagram shows a sector $OAB$ of a circle, centre $O$, with $OA = OB = 8$ cm and angle $AOB = 160^\circ$. $AB$ is a chord.
    Work out the area of the shaded segment (between the chord $AB$ and the arc).
24. 24The diagram shows a sector $OAB$ of a circle, centre $O$, with $OA = OB = 11$ cm and angle $AOB = 110^\circ$. $AB$ is a chord.
    Work out the area of the shaded segment (between the chord $AB$ and the arc).