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

2 hours26 questions
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1
Sme Calculator2 marks

The diagram below shows two types of line associated with circles.

Write down the name of line a and the name of line b.

Circle with a line labelled a going from a point on the circumference to the centre and a line labelled b going between two different points on the circumference

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2
Sme Calculator2 marks

A circle has a radius of 12 cm.

Find the exact value of the area of the circle.

Give your answer in terms of pi. 

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

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3
Sme Calculator4 marks

The diagram below shows a circle with a circular hole.

The shape is made by starting with a circle of radius 10 cm, and then a smaller circle of radius 2 cm is removed.

Find the shaded area of the shape.

Write your answer to 3 significant figures.

A circle of 10 cm radius shaded grey, with a second unshaded circle of radius 2 cm inside the larger circle

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4
Sme Calculator6 marks

The diagram shows a sector O A B C.

circles-easy-140-sector

Find, giving your answers to 3 significant figures:

(i) The area of the sector O A B C.

[3]

(ii) The length of the arc A B C.

[3]

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5
Sme Calculator3 marks

A circle has diameter 6 cm.

Calculate the area of the circle.
Give the units of your answer.

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6
Sme Calculator2 marks

Calculate the area of a circle with radius 12cm.

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

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7
Sme Calculator2 marks

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

Calculate the circumference of the mirror.

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

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8
Sme Calculator2 marks

Calculate the circumference of a circle with radius 4.5cm.

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

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9
Sme Calculator2 marks

A circle has diameter 7 cm.

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

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1
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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".

Two circles with the centre points marked

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2
Sme Calculator2 marks

The diagram below shows a semicircle with diameter 50 m.

Find the perimeter of the semicircle.

Give your answer in an exact form.

Semicircle with diameter 50 m

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3
Sme Calculator5 marks

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.

An isosceles triangle of height 100 cm with the flat edge of a semicircle of radius 30 cm attached to the shortest edge of the triangle

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

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4a
Sme Calculator3 marks

The diagram below shows sector O A B C.

Given that the area of the sector O A B C is 48 pi cm2, find the value of r.

Circle with centre O and points A, B and C marked on the circumference of the circle, a sector is marked between A, O and C with an angle of 120 degrees and a radius of r cm

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4b
Sme Calculator3 marks

The diagram below shows sector O P Q R.

Given that the length of the arc P Q R is 10 pi cm, find the value of theta.

Circle with centre O and points P, Q and R marked on the circumference of the circle, a sector arc is marked between P, O and R with an angle of θ degrees and a radius of 18 cm

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5
Sme Calculator2 marks

A circle has a circumference of 56mm.

Work out the radius of this circle.

.............................mm 

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6
Sme Calculator3 marks

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

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7
Sme Calculator2 marks
qp28-0580-01-paper-1-specimen-2020-cie-igcse-maths

O A B 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 

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8
Sme Calculator3 marks
q21-058012-mayjune2019-cie-igcse-maths-core

The diagram shows a semicircle with diameter 9 cm.

Calculate the total perimeter of this semicircle.

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

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9
Sme Calculator4 marks

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]

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1
Sme Calculator3 marks

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.

 

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2
Sme Calculator4 marks

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.

circles-hard-q2

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

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3
Sme Calculator4 marks

The diagram shows a sector O A B C of a circle, centre O and radius 6 cm.

Circle with centre O and points A, B and C marked on the circumference. A right-angled triangle is formed between A, O and C and the radius is 6 cm

O A C is a right-angled triangle.

Work out the area of the shaded segment A B C.

Give your answer to 3 significant figures.

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

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4a
Sme Calculator4 marks

The shaded shape below, A P Q B, is formed by taking a large sector, O P Q, and removing a smaller sector, O A B.

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

Sector OAB with angle 60 degrees and radius 18 cm overlaid by sector OPQ with the same angle and a radius 6 cm longer. The area APQB is shaded.

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4b
Sme Calculator5 marks

For the same shape described in part (a)

Sector OAB with angle 60 degrees and radius 18 cm overlaid by sector OPQ with the same angle and a radius 6 cm longer. The area APQB is shaded.

Find the perimeter of the shape A P Q B, stating your answer in terms of straight pi.

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5a
Sme Calculator1 mark
qp6-0580-31-paper-3-may-2020-cie-igcse-maths

The diagram shows a circle, centre O, radius 11 cm. C comma space F comma space G and H are points on the circumference of the circle.
The line A D touches the circle at C and is parallel to the line E G. B is a point on A D and angle A B O = 140°.

Write down the mathematical name of the straight linespace A D.

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5b
Sme Calculator6 marks

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

[2]

ii) Work out angle F O H.

Angle F O H = ................................................. [2]

iii) Calculate the length of the minor arc F H.

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

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6
Sme Calculator5 marks
qp7d-0580-32-paper-3-may-2020-cie-igcse-maths

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 

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7
Sme Calculator8 marks

The diagram shows a rectangle and two semicircles with diameters A C and B D.
This diagram is a scale drawing of a running track.

A C space equals space B D space equals space 60 straight m space A B space equals space C D space equals space 120 straight m

q9-058032-march2019-cie-igcse-maths-core

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]

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8
Sme Calculator3 marks
q10e-058032-march2019-cie-igcse-maths-core

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 

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