Circles, Arcs & Sectors (Cambridge International IGCSE Mathematics): Exam Questions

A circle has diameter 6 cm.

Calculate the area of the circle.

Give the units of your answer.

Calculate the area of a circle with radius 12cm.

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

Henry buys a circular mirror for the room. The diameter of the mirror is 80 cm.

Calculate the circumference of the mirror.

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

Calculate the circumference of a circle with radius 4.5cm.

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

A circle has diameter 7 cm.

Show that the circumference of the circle is 21.99cm, correct to 2 decimal places.

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 $π$.

......................................... 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$AD$.

Extract:

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

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

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. $AC=BD=60m\,AB=CD=120m$

i) Complete the statement.

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

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