IGCSEMathsCambridge (CIE)ExtendedExam QuestionsLengths, Areas & VolumesCircles, Arcs & Sectors

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

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Circles, Arcs & Sectors

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Circles, Arcs & Sectors

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1
Sme Calculator3 marks
q8-paper2-spec2025-cie-igcse-further-maths

The diagram shows a semicircle with diameter 9cm.

Calculate the total perimeter of this semicircle.

Give your answer in exact form.

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2
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q3-4-6-easy-edexcel-gcse-maths

O A B is a sector of a circle, centre O.

The radius of the circle is 15 cm.

The angle of the sector is 30 degree.

Calculate the area of sector O A B.

Give your answer as a simplified expression in terms of straight pi.

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3
Sme Calculator2 marks

The diagram shows a sector of a circle of radius 7 cm.

q4-4-6-easy-edexcel-gcse-maths

Work out the length of arc A B.

Give your answer as a simplified expression in terms of straight pi.

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4
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 as a simplified expression in terms of straight pi.

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

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5
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 as a simplified expression in terms of straight pi.

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

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1
Sme Calculator3 marks
cie-igcse-2019-oct-nov-p2-tz1-q17

The diagram shows two sectors of circles with the same centre. Calculate the shaded area.

Give your answer in terms of straight pi.

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

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2
Sme Calculator3 marks
cie-igcse-2018-oct-nov-p2-tz3-q19

The diagram shows a sector of a circle with radius 6 cm and sector angle 72°.

The perimeter of this sector is  left parenthesis p plus q straight pi right parenthesis cm. Find the value of p and the value of q.

p = ................................................ 

    q = ................................................     

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3
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The diagram shows a square A B C D inside a circle.

q10-4-6-medium-edexcel-gcse-maths

The points A comma space B comma space C and D lie on the circle.

The radius of the circle is 6 cm.

Work out the total area of the shaded regions.

Give your answer in terms of straight pi.

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4
Sme Calculator5 marks
~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 as an exact value in terms of straight pi.

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1a
Sme Calculator3 marks
cie-igcse-2020-oct-nov-p2-tz3-q21

OAB is the sector of a circle, centre O.

OB = 8 cm and angle AOB = 30°.

BP is perpendicular to OA.

Calculate AP.

Give your answer as an exact value.  

AP =  ........................................... cm

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1b
Sme Calculator3 marks

Work out the area of the shaded region APB. Give your answer as an exact value in terms of straight pi.  

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

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2
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A B is an arc of a circle, centre O, radius 9 cm. 

cie-igcse-q23-arc-sector

The length of the arc A B is 6 straight pi cm.

The area of sector A O B is k straight pi cm2.

Find the value of k.

k space= ..............................................

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3
Sme Calculator4 marks
cie-igcse-2018-oct-nov-p2-tz2-q21

The diagram shows an equilateral triangle ABC with sides of length 10 cm.

AMN is a sector of a circle, centre A.

M is the mid-point of AC.

Work out the area of the shaded region.

Give your answer as an exact value in terms of straight pi.  

......................................... 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. Give your answer as a simplified expression in terms of straight pi.  

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

ii) Calculate the perimeter of the shaded segment. Give your answer as a simplified expression in terms of straight pi.  

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

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