Circles, Arcs & Sectors (Cambridge (CIE) IGCSE Maths: Core): Exam Questions

A circle has a circumference of 56mm.

Work out the radius of this circle.

.............................mm 

Rachel has a pond in her garden in the shape of a circle.
The circumference of the pond is 4.25m.

Calculate the diameter of the pond.
Give your answer in centimetres.

............................................ cm

$OAB$ is a sector of a circle with radius 9 cm and centre $O$.
The angle at $O$ is 30°.

Calculate the area of this sector.
Give your answer in terms of $\pi$.

......................................... cm² 

The diagram shows a semicircle with diameter 9 cm.

Calculate the total perimeter of this semicircle.

......................................... cm 

There is a circular pool in the play area at a park.
The pool has a diameter of 8m.

Calculate

i) the circumference of the pool,

..........................m [2]

ii) the area of the pool.

........................... m² [2]

The diagram shows a circle, centre $O$, radius 11 cm. $C,F,G$ and $H$ are points on the circumference of the circle.

The line $AD$ touches the circle at $C$ and is parallel to the line $EG$.

$B$ is a point on $AD$ and angle $ABO$ = 140°.

Write down the mathematical name of the straight line$AD$.

i) Find, in terms of $\pi$, the circumference of the circle.

[2]

ii)Work out angle $FOH$.

Angle $FOH$ = ................................................. [2]

iii) Calculate the length of the minor arc $FH$.

............................................ cm [2]

The diagram shows a square with vertices on the circumference of a circle, centre $O$.
The radius of the circle is 6 cm.

Work out the shaded area.

.......................................... cm² 

Points $P,Q$ and $R$ are on the circumference of a semicircle, centre $O$ and radius 8 cm.
Angle $POQ$ = 90°.

Calculate the shaded area.

.........................................cm² 

The diagram shows a rectangle and two semicircles with diameters $AC$ and $BD$.
This diagram is a scale drawing of a running track. $$\begin{gathered} AC=BD=60\mathrm{m} \\ AB=CD=120\mathrm{m} \end{gathered}$$

i) Complete the statement.

1 centimetre represents ............................ metres.

[2]

ii) Work out the total length of the running track in metres.

............................. m [3]

iii) Shreva walks at 1.4m/s.

Work out how long it will take her to walk once around the track. Give your answer in minutes and seconds, correct to the nearest second.

.................... minutes .................... seconds [3]

This shape is drawn using two semicircles that have the same centre.

The large semicircle has radius 7 cm.

The small semicircle has radius 3 cm.

Calculate the area of the shape.

.............................. cm² 

Points $A$ and $B$ lie on the circle.
A region has been shaded between line $AB$ and the circumference of the circle.

The area of the circle is 76.4 cm².

Calculate the radius of the circle.

.......................................... cm

The diameter of a different circle is 38 mm.

Calculate the circumference of this circle.
Give your answer in centimetres.

.......................................... cm