Geometry · Guided Practice

Arcs and Sectors

16 questions with answers and video solutions. Try each one before revealing the answer.

1
A sector has radius 5 cm. The angle at its centre is 41°. Calculate:
  (a)  the arc length
  (b)  the sector area.

No hints on this one — its full written solution is with the answer.

2

A sector has radius 3 cm. The angle at its centre is 120°. Find:
  (a)  the arc length
  (b)  the sector area.
Use 3.14 as an approximation of π.\displaystyle \pi.

No hints on this one — its full written solution is with the answer.

3

A sector has radius 50 cm. The angle at its centre is 72°. Find:
  (a)  the arc length
  (b)  the sector area.
Use 3.14 as an approximation of π.\displaystyle \pi.

No hints on this one — its full written solution is with the answer.

4
A sector has arc length 12 cm and radius 7 cm.
Calculate the angle a∘\displaystyle a^\circ at the centre.

No hints on this one — its full written solution is with the answer.

5
A sector has area 115 mm2 and radius 8 mm.
Calculate the angle a∘\displaystyle a^\circ at the centre.

No hints on this one — its full written solution is with the answer.

6
A sector has arc length 7.79 cm. The angle at the centre is 72°.
Calculate the radius.

No hints on this one — its full written solution is with the answer.

7
A sector has area 17.3 cm2. The angle at the centre is 153°.
Calculate the radius.

No hints on this one — its full written solution is with the answer.

8
A sector has radius 5 cm and arc length 6.28 cm. Calculate the angle a∘\displaystyle a^\circ at the centre.
Use π≈\displaystyle \pi\approx 3.14.

No hints on this one — its full written solution is with the answer.

9
2015 P2 Q10
4 Marks

The pendulum of a clock swings along an arc of a circle, centre O.

Pendulum swinging along an arc

The pendulum swings through an angle of 65°, travelling from A to B.
The length of the arc AB is 28.4 centimetres.
Calculate the length of the pendulum.

10
2016 P1 Q3
3 Marks

The diagram shows a sector of a circle, centre C.

Sector of a circle with radius 20cm and angle 45 degrees

The radius of the circle is 20 centimetres and angle ACB is 45∘\displaystyle 45^{\circ}.
Calculate the area of the sector.
Take π=3⋅14\displaystyle \pi=3\cdot14.

11
2017 P2 Q14
3 Marks

The diagram shows part of a circle, centre O.
The radius of the circle is 6.4 cm.
Major arc AB has length 31.5 cm.

Circle with major arc

Calculate the size of the reflex angle AOB.

12
2018 P2 Q2
3 Marks

The diagram below shows a sector of a circle, centre C.

Sector of a circle with angle 320 degrees

The radius of the circle is 7.4 centimetres.
Angle ACB is 320∘\displaystyle 320^{\circ}.
Calculate the length of the major arc AB.

13
2019 P1 Q4
3 Marks

The diagram below shows a sector of a circle, centre C.

Sector of a circle with angle 240 degrees and radius 30cm

The radius of the circle is 30 centimetres.
Calculate the length of the major arc AB.
Take π=3⋅14.\displaystyle \pi=3\cdot14.

14
2023 P2 Q3
3 Marks

The diagram shows part of a football pitch.

Part of a football pitch with an arc

The penalty spot is marked at point C.
AB is an arc of a circle, centre C, radius 9.15 metres.
Calculate the length of the arc AB.

15
2024 P2 Q15
3 Marks

The diagram shows a sector of a circle, centre C.

Sector of a circle

The radius of the circle is 12 centimetres.
The length of arc AB is 15 centimetres.
Calculate the area of the sector.

16
2025 P2 Q6
3 Marks

A party hat is made in the shape of a cone, as shown.

Cone party hat

The piece of card used for making the hat is a sector of a circle, centre C.

Sector of circle

The radius of the circle is 15 centimetres and angle ACB is 170°.
Calculate the area of the sector.

Keep practising

More arcs and sectors questions

New questions, modelled on past paper questions and checked against their marking instructions. Not reprints — you have not seen these before.

Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.

All practice topics