Sector Areas and Arc Lengths worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 26 marks Sheet 1

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2 marks
The diagram shows a sector of a circle with centre \(O\).

The radius is \(12\) cm and the angle of the sector is \(120^\circ\).

Work out the length of the arc \(AB\). Give your answer in terms of \(\pi\).
2 marks
Here is a sector of a circle with centre \(O\) and radius \(4\) cm.

The angle of the sector is \(270^\circ\).

Find the area of the sector. Give your answer in terms of \(\pi\).
3 marks
(a)
The shaded sector \(AOB\) has an angle of \(135^\circ\).

Write down the size of the reflex angle \(AOB\).

(b)
Find the area of the unshaded part of the circle. Give your answer in terms of \(\pi\).
3 marks
The diagram shows a sector \(AOB\) of a circle with centre \(O\).

\(OA = OB = 6\) cm and angle \(AOB = 60^\circ\).

Find the perimeter of the sector. Give your answer in terms of \(\pi\).
3 marks
The diagram shows a sector of a circle with centre \(O\) and radius \(10\) cm.

The length of the arc \(AB\) is \(5\pi\) cm.

Find the size of the angle marked \(x\).
2 marks
The diagram shows a sector of a circle with centre \(O\).

The radius is \(6\) cm and the angle of the sector is \(60^\circ\).

Calculate the length of the arc \(AB\). Give your answer in terms of \(\pi\).
2 marks
Here is a sector of a circle with centre \(O\) and radius \(12\) cm.

The angle of the sector is \(45^\circ\).

Find the area of the sector. Give your answer in terms of \(\pi\).
3 marks
(a)
The shaded sector \(AOB\) has an angle of \(120^\circ\).

State the size of the reflex angle \(AOB\).

(b)
Work out the area of the unshaded part of the circle. Give your answer in terms of \(\pi\).
3 marks
Here is a sector \(AOB\) of a circle with centre \(O\).

\(OA = OB = 6\) cm and angle \(AOB = 150^\circ\).

Find the perimeter of the sector. Give your answer in terms of \(\pi\).
3 marks
The diagram shows a sector of a circle with centre \(O\) and radius \(8\) cm.

The length of the arc \(AB\) is \(6\pi\) cm.

Work out the size of the angle marked \(x\).

Answers

\(8\pi\ \text{cm}\)
\(12\pi\ \text{cm}^2\)
(a) \(225^\circ\)
(b) \(40\pi\ \text{cm}^2\)
\((2\pi + 12)\ \text{cm}\)
\(90^\circ\)
\(2\pi\ \text{cm}\)
\(18\pi\ \text{cm}^2\)
(a) \(240^\circ\)
(b) \(24\pi\ \text{cm}^2\)
\((5\pi + 12)\ \text{cm}\)
\(135^\circ\)

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