O LevelMathsCambridgeExam QuestionsLengths, Areas & VolumesCircles, Arcs & Sectors

Circles, Arcs & Sectors (Cambridge O Level Maths)

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Circles, Arcs & Sectors

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Circles, Arcs & Sectors

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1
Sme Calculator2 marks

cie-igcse-2020-oct-nov-p2-tz2-q15

Calculate the area of this sector of a circle.


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

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2
Sme Calculator2 marks

cie-igcse-2019-may-jun-p2-tz3-q12

The diagram shows a sector of a circle with radius 6.2 cm and sector angle 217°.

Calculate the area of this sector.
 

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

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3
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Calculate the area of a circle with radius 5.1 cm.

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

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4
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The diagram shows a sector of a circle of radius 4 cm.

q5-4-6-easy-edexcel-gcse-maths

Work out the length of the arc A B C.
Give your answer correct to 3 significant figures.

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5
Sme Calculator2 marks

The diagram shows sector space O P Q spaceof a circle, centre O

q11-4ma1-1hr-qp-jan22-paper1-igcse-maths-1

O P space equals space O Q space equals space 7.1 space cm
Angle P O Q space equals space 110 degree

Calculate the area of sector O P Q
Give your answer correct to one decimal place.

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6
Sme Calculator3 marks

cie-igcse-2020-may-june-p4-tz1-q9a

The diagram shows a sector of a circle with centre O, radius 8 cm and sector angle 165°.

Calculate the total perimeter of the sector.


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

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7
Sme Calculator3 marks

cie-igcse-2019-may-jun-p4-tz1-q5a

 
The diagram shows the surface of a garden pond, made from a rectangle and two semicircles.
The rectangle measures 3 m by 1.2 m.

Calculate the area of this surface.
 

...............................................m2

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8a
Sme Calculator7 marks

cie-igcse-2018-oct-nov-p4-tz2-q10aiii

The cross-section of a gate is a sector of a circle with radius 8.5 m and angle 76°.
 
Calculate the perimeter of the sector.
 

............................................ m

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8b
Sme Calculator6 marks

cie-igcse-2018-oct-nov-p4-tz2-q10b

A solid metal cone has radius 10 cm and height 36 cm.

i)
Calculate the volume of this cone.
[The volume, V, of a cone with radius r and height h is  V equals 1 third straight pi r squared h.]
 
 

......................................... cm3[2]

ii)
The cone is cut, parallel to its base, to give a smaller cone.
cie-igcse-2018-oct-nov-p4-tz2-q10bii
The volume of the smaller cone is half the volume of the original cone.
The smaller cone is melted down to make two different spheres.
The ratio of the radii of these two spheres is 1 : 2.

Calculate the radius of the smaller sphere.
[The volume, V, of a sphere with radius r is  V equals 4 over 3 straight pi r cubed.]
 
 

.......................................... cm [4]

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9
Sme Calculator4 marks

The diagram shows the top of Levi's birthday cake.

q10-4-6-easy-edexcel-gcse-maths

The top of the cake is in the shape of a circle.
The diameter of the circle is 7 inches.

A ribbon is going to be put around the side of the cake.
Ribbons are sold in 50 cm lengths.

1 inch is 2.54 cm.

Work out if one length of ribbon is long enough to go all the way around the cake.
You must show your working.

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10
Sme Calculator4 marks

O A B is a sector of a circle with centre O and radius 7 cm.

bV5GMp8X_q6-4-6-medium-edexcel-gcse-maths

The area of the sector is 40 cm2.

Calculate the perimeter of the sector.
Give your answer correct to 3 significant figures.

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11
Sme Calculator4 marks

The diagram shows a circle with centre O

q16-january-2022-1h-edexcel-igcse-maths

A comma space B and space C spaceare points on the circle so that the length of the arc A B C is 5 cm.

Given that angle A O C = 55°

work out the area of the circle.
Give your answer correct to one decimal place.

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12
Sme Calculator3 marks

The diagram shows Yuen’s garden.

q5-4ma1-1hr-qp-jan20-paper1-igcse-maths

The garden is in the shape of a semicircle of radius 7.2 straight m.
Yuen is going to cover his garden with grass seed.

Yuen has 12 boxes of grass seed.
Each box of grass seed contains enough seed to cover 6 straight m squared of the garden.

Has Yuen enough grass seed for his garden?
Show your working clearly.

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1
Sme Calculator3 marks

Calculate the area of the sector of a circle with radius 65 mm and sector angle 42°.
Give your answer in square centimetres.
 

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

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2
Sme Calculator3 marks

q12-4-6-medium-edexcel-gcse-maths

The arc A B C is a quarter of a circle with centre O and radius 4.8 cm.
A C is a chord of the circle.

Work out the area of the shaded segment.
Give your answer correct to 3 significant figures.

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3
Sme Calculator3 marks

q13-4-6-medium-edexcel-gcse-maths

O A B is a sector of a circle, centre O.
O C D is a sector of a circle, centre O.
O C A and O D B are straight lines.

Angle A O B space equals space 75 degree
O D space equals space 6 space cm space D B space equals space 4 space cm

Calculate the perimeter of the shaded region.
Give your answer correct to 3 significant figures.

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4
Sme Calculator5 marks

q9-4-6-medium-edexcel-gcse-maths

O N Q is a sector of a circle with centre O and radius 11 cm.

A is the point on O N and B is the point on O Q such that A O B is an equilateral triangle of side 7 cm.

Calculate the area of the shaded region as a percentage of the area of the sector O N Q.
Give your answer correct to 1 decimal place.

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5
Sme Calculator5 marks

The diagram shows a shaded shape space A B C D spacemade from a semicircle space A B C spaceand a right-angled triangle A C D.

q11-4ma1-2h-qp-jan20-paper2-igcse-maths

A C spaceis the diameter of the semicircle A B C.

Work out the perimeter of the shaded shape.
Give your answer correct to 3 significant figures.

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

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6
Sme Calculator3 marks

cie-igcse-2020-oct-nov-p4-tz1-q4d

The diagram shows a square with side length 8 cm and a sector of a circle with radius 9.5 cm and sector angle x°.
The perimeter of the square is equal to the perimeter of the sector.

Calculate the value of x.

x space equals ................................................

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7
Sme Calculator9 marks

cie-igcse-2019-oct-nov-p4-tz3-q6a

In the diagram, A, B, C and D lie on the circle, centre O.
Angle ADC = 128°, angle ACD = 28° and angle BCO = 30°.

The radius, OC, of the circle is 9.6 cm.

Calculate the total perimeter of the sector OADC.
 

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

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8
Sme Calculator4 marks

cie-igcse-2019-may-jun-p4-tz2-q8b

The diagram shows a sector of a circle of radius 3.8 space text cm end text.
The arc length is 7.7 space text cm end text.

i)
Calculate the value of y.
 
y = .............................................. [2]
ii)
Calculate the area of the sector.
 
........................................ cm2 [2]

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9a
Sme Calculator5 marks

cie-igcse-2018-may-jun-1-8c

P, Q and R are points on the circumference of the circle, centre O.
PO is parallel to QR and angle POQ = 48°.

Find angle OPR.

Angle OPR = ...............................................

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9b
Sme Calculator5 marks

The radius of the circle is 5.4 cm.
Calculate the length of the major arc PQ.


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

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10
Sme Calculator5 marks

The diagram shows a plan of Brian's lawn.

q7-4-6-medium-edexcel-gcse-maths

The edge of the lawn consists of two semicircles and two straight lines.
Each semicircle has centre O.
The diameters of the semicircles are 9 m and 5 m.

Brian is going to put lawn edging around the edge of the lawn.
Lawn edging is sold in 2.4 metre rolls.

Brian has £35

Lawn edging

£3.99 per roll
or
3 rolls for £10

Has Brian got enough money to buy all the rolls of lawn edging he needs?
You must show all your working.

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11
Sme Calculator4 marks

Saphia is organising a conference.

People at the conference will sit at circular tables.

q8-4-6-medium-edexcel-gcse-maths

Each table has a diameter of 140 cm.
Each person needs 60 cm around the circumference of the table.

There are 12 of these tables in the conference room.
A total of 90 people will be at the conference.

Are there enough tables in the conference room?

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12
Sme Calculator5 marks

q14-4-6-medium-edexcel-gcse-maths

A comma space B and C are points on a circle of radius 5 cm, centre O.
D A and D C are tangents to the circle.
D O space equals space 9 space cm

Work out the length of arc A B C.
Give your answer correct to 3 significant figures.

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1
Sme Calculator4 marks

cie-igcse-2020-mary-jun-p2-tz2-q24

The diagram shows a sector of a circle of radius 8 cm.
The length of the arc P Q is 6.4 cm.
 
Find the area of the sector.
 

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

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2
Sme Calculator3 marks

The total perimeter of a semicircle is 19.02 cm.
 
Calculate the radius of the semicircle.
 

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

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3
Sme Calculator8 marks

cie-igcse-2019-oct-nov-p4-tz2-q8b

A and B lie on a circle, centre O.

Calculate the length of the arc A B.

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4a
Sme Calculator5 marks

cie-igcse-2019-march-p4-q6

The diagram shows a company logo made from a rectangle and a major sector of a circle.
The circle has centre O and radius OA.
OA = OD = 0.5 cm and AB = 1.5 cm.
E is a point on OC such that OE = 0.25 cm and angle OED = 90°.

Calculate the perimeter of the logo.
 

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

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4b
Sme Calculator3 marks

Calculate the area of the logo.
 

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

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5a
Sme Calculator5 marks

h0KYsqUX_cie-igcse-2018-oct-nov-p4-tz1-q10a

The diagram shows a circle, centre O.
The straight line ABC is a tangent to the circle at B.
OB = 8 cm, AB = 15 cm and BC = 22.4 cm.
AO crosses the circle at X and OC crosses the circle at Y.
 
Calculate angle XOY.
 

Angle XOY = ...............................................

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5b
Sme Calculator2 marks

Calculate the length of the arc XBY.
 

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

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5c
Sme Calculator4 marks

Calculate the total area of the two shaded regions.
 

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

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6a
Sme Calculator4 marks

cie-igcse-2018-may-jun-2-p4-q5

The diagram shows a design made from a triangle AOC joined to a sector OCB.
AC = 8cm, OB = OC = 7 cm and angle ACO = 78°.

Use the cosine rule to show that OA = 9.47 cm, correct to 2 decimal places.

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6b
Sme Calculator3 marks

Calculate angle OAC.

Angle OAC = ................................................

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6c
Sme Calculator5 marks

The perimeter of the design is 29.5 cm.

Show that angle COB = 41.2°, correct to 1 decimal place.

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6d
Sme Calculator4 marks

Calculate the total area of the design.

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

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7
Sme Calculator3 marks

Maya builds a patio in her garden in the shape of a cylinder, with radius 2m and a height of 0.08m.
Maya wants to put tiles on the surface of her patio, as shown on the diagram.
Each tile is a sector with arc length 75cm.

q11b-specimen-paper2-2025-4024-02-cambridge-o-level-maths-d

Explain why the tiles do not fit exactly on the surface of the patio.

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8
Sme Calculator5 marks

P and Q are points on the circle centre O with radius 4 cm.
P Ô Q = 130°.

q8b-june-2018-4024-2-cambridge-o-level-maths-d

i)
Calculate the area of triangle P O Q.

...............cm2[2]

ii)
Calculate the area of the major segment, shown unshaded in the diagram.

.............cm2[3]

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