GCSEMathsOCRFoundationExam Questions10. Mensuration, Lengths, Areas & VolumesCircles, Arcs & Sectors

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

Exam code: J560

2 hours29 questions
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1
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2 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
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2 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
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4 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
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6 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
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3 marks

A circle has diameter 6 cm.

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

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6
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2 marks

Calculate the area of a circle with radius 12cm.

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

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7
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2 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
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2 marks

Calculate the circumference of a circle with radius 4.5cm.

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

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9
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2 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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10a
1 mark

The diagram shows a circle, centre O, and a line that meets the circle twice.

A circle with its centre point marked as a labelled dot "O". A diagonal straight line is drawn across the circle passing through O, with its two endpoints on the circumference.

On the diagram, draw a chord.

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10b
1 mark

Write down the mathematical name of the line shown on the diagram.

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1
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2 marks

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
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2 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
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5 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
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3 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
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3 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
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2 marks

A circle has a circumference of 56mm.

Work out the radius of this circle.

.............................mm 

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6
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3 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
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2 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
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3 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
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4 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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10
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4 marks

A circle has an area of 50 cm².

Show that the circumference of the circle is 25.1 cm, correct to 3 significant figures.

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1
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3 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
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4 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
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4 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
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4 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
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5 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
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1 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
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6 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
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5 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
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8 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
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3 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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9
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5 marks

The diagram shows a shaded shape made by removing sector OAB from sector OCD.

Both sectors have an angle of 45°.

The radius, OA, of the smaller sector is r \text{ cm}.

The ratio of radius OA to radius OC is 1 : 3.

A diagram of two concentric sectors sharing the same centre O. The smaller sector OAB has radius OA = r and angle 45° at O. The larger sector OCD has the same centre O, the same 45° angle, but a larger radius OC. The region between the two arcs (i.e., the curvy "ring slice" bounded by AB on the inside, CD on the outside, and the two radial straight lines AC and BD) is shaded. The angle at O is marked 45° between the two radii. Vertices labelled A, B on the smaller arc and C, D on the larger arc, with O at the centre. The text "Not to scale" floats to the top right.

Work out, in terms of \pi and r, the perimeter of the shaded shape A C D B.

Give your answer in its simplest form.

You must show your working.

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