IGCSEMaths: ExtendedCIETopic Questions3. Geometry3.6 Circles, Arcs & Sectors

Syllabus Edition

First teaching 2021

Last exams 2024

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Circles, Arcs & Sectors (CIE IGCSE Maths: Extended)

Topic Questions

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1
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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2
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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3a
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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3b
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The radius of the circle is 5.4 cm.
Calculate the length of the major arc PQ.


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

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4
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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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5
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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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6
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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7
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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8
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~35-_5Zr_q9-4-6-medium-edexcel-gcse-maths

O A C is a sector of a circle, centre O, radius 10 m.

B A is the tangent to the circle at point A.
B C is the tangent to the circle at point C.

Angle A O C equals space 120 degree

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

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1
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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2
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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3
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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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4
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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5
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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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6
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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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7
Sme Calculator3 marks

The region, shown shaded in the diagram, is a path.

q8-4ma1-1h-qp-jan21-paper1-igcse-maths

The boundary of the path is formed by two semicircles, with the same centre O, and two straight lines.

The inner semicircle has a radius of 7 metres.
The path has a width of 2 metres.

Work out the perimeter of the path.
Give your answer correct to one decimal place.

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

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8
Sme Calculator4 marks

A circle centre O has radius 9 cm.

q11-4ma1-2hr-qp-jan21-paper2-igcse-maths

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

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

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9
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 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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2a
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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2b
Sme Calculator3 marks

Calculate the area of the logo.
 

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

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3a
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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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3b
Sme Calculator2 marks

Calculate the length of the arc XBY.
 

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

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3c
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Calculate the total area of the two shaded regions.
 

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

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4a
Sme Calculator2 marks

cie-igcse-2018-march-p4-q2

The vertices of a square ABCD lie on the circumference of a circle, radius 8 cm.
 
Calculate the area of the square.
 

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

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4b
Sme Calculator7 marks

i)

Calculate the area of the shaded segment.
 

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

ii)

Calculate the perimeter of the shaded segment.
 

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

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5a
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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5b
Sme Calculator3 marks

Calculate angle OAC.

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

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5c
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The perimeter of the design is 29.5 cm.

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

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5d
Sme Calculator4 marks

Calculate the total area of the design.

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

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