Circles, Arcs & Sectors (AQA GCSE Maths: Foundation): Exam Questions

On the left circle below, draw a sector and shade it in. Label it "sector".

On the right circle below, draw a segment and shade it in. Label it "segment".

The diagram below shows a semicircle with diameter 50 m.

Find the perimeter of the semicircle.

Give your answer in an exact form.

A new sign for an ice cream shop has been designed.

It consists of a semicircle and an isosceles triangle.

The dimensions of the sign are shown in the diagram below.

Calculate the total area of the sign to 3 significant figures.

.................... cm²

The diagram below shows sector $OABC$.

Given that the area of the sector $OABC$ is $48\pi$ cm², find the value of $r$.

The diagram below shows sector $OPQR$.

Given that the length of the arc $PQR$ is $10\pi$ cm, find the value of $\theta$.

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]

A circle has a diameter of 9 cm.

Work out $\frac{3}{4}$ of its area.

Give your answer in terms of $\pi$.

Two identical circles with a diameter of 17 cm fit perfectly inside a rectangle.

Work out the area of the rectangle. Give your answer in square metres.

Work out the area of the shaded region.

Give your answer in square centimetres to 1 decimal place.

Write down the mathematical terms associated with circles that can be described by the following definitions:

(i) A line passing through the centre of the circle, which intersects the circle in one place only.

(ii) An area formed by two radii.

(iii) An area formed by a chord.

The diagram below shows a semicircle and a circle.

The diameter of the semicircle is 16 cm.

The radius of the circle is $r$ cm.

Given that the area of the semicircle is 8 times larger than the area of the circle, find the value of $r$.

The diagram shows a sector $OABC$ of a circle, centre $O$ and radius 6 cm.

$OAC$ is a right-angled triangle.

Work out the area of the shaded segment $ABC$.

Give your answer to 3 significant figures.

...................... cm²

The shaded shape below, $APQB$, is formed by taking a large sector, $OPQ$, and removing a smaller sector, $OAB$.

Find the shaded area, stating your answer in terms of $\pi$.

For the same shape described in part (a)

Find the perimeter of the shape $APQB$, stating your answer in terms of $\mathrm{\pi }$.

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 

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