1
Arcs & Sectors
Exercise 1
Question 1
[OCR GCSE(9-1) Practice set 1 6H Q7]
OPQ is a sector of a circle, centre O and
radius 9 cm.
The diagram shows a sector of a circle,
centre O. The radius of the circle is 9
cm. The angle at the centre of the circle
is 40°.
Find the perimeter of the sector.
Leave your answer in terms of 𝜋.
Question 4
[Edexcel IGCSE June2010-4H Q17] The
diagram shows a sector of a circle, radius
45 cm, with angle 84°.
Find the perimeter of the sector.
Give your answer in terms of 𝜋.
Question 2
[AQA GCSE Nov 2012 2H Q23] The
diagram shows a sector of a circle.
Calculate the area of the sector. Give
your answer correct to 3 significant
figures.
Question 5
[Edexcel IGCSE Jan2017-3H Q22]
Work out the area of the sector.
Give your answer to a suitable degree
of accuracy.
Question 3
[Edexcel GCSE June2003-5H Q15]
The diagram shows a sector OAB of a
circle, centre O. Angle AOB = 75°
Length of arc AB = 7.2 cm
Calculate the area of the sector.
Give your answer correct to 3
significant figures.
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2
Question 6
Question 8
[AQA GCSE June 2016 2H Q17] The
diagram shows a sector of a circle.
The radius is 7 𝑐𝑚.
[OCR GCSE(9-1) Nov 2017 6H Q8] The
Work out the perimeter of the shape.
Question 7
[AQA GCSE Nov 2016 1H Q21] This
shape is made from two identical sectors.
design below is made from two sectors of
circles, centre 𝑂.
Calculate the perimeter of the shaded
part. Give your answer correct to 3
significant figures.
Exercise 2
Test Your Understanding
[Edexcel IGCSE Jan2016-4H Q24] The
diagram shows sector OAB of a circle,
centre 𝑂.
Work out the perimeter of the shape.
Give your answer in terms of 𝜋.
Angle 𝐴𝑂𝐵 = 50° Sector 𝑂𝐴𝐵 has area
20𝜋 cm2
Calculate the perimeter of sector 𝑂𝐴𝐵 .
Give your answer correct to 3
significant figures.
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3
Question 1
Question 4
[Edexcel GCSE March2013-2H Q19] OAB is
a sector of a circle, centre O.
The radius of the circle is 15 cm.
The angle of the sector is 30°.
[Edexcel GCSE(9-1) Nov 2018 3H Q16] Here
is a shaded shape 𝐴𝐵𝐶𝐷.
Calculate the area of sector OAB.
Give your answer correct to 3 significant
figures.
Question 2
[OCR GCSE(9-1) Nov 2018 5H Q12] 𝐴𝑂𝐵 is a
sector of a circle, centre 𝑂 and radius 6 cm.
The length of arc 𝐴𝐵 is 5𝜋 cm.
The shape is made from a triangle and a
sector of a circle, centre 𝑂 and radius 6 cm.
𝑂𝐶𝐷 is a straight line. 𝐴𝐷 = 14 cm
Angle 𝐴𝑂𝐷 = 140 Angle 𝑂𝐴𝐷 = 24
Calculate the perimeter of the shape. Give
your answer correct to 3 significant figures.
Question 5
[Edexcel IGCSE Nov2009-3H Q18] In the
diagram, a sector of a circle of radius 12 cm
is shaded. The area of the sector is
112𝜋 𝑐𝑚 2 . Calculate the value of 𝑥.
Find the area of the sector.
Give your answer in terms of 𝜋.
Question 3
Question 6
[OCR GCSE June 2016 3H Q20] OAB is a
sector of a circle, centre O.
Angle AOB = 120°.
[Edexcel GCSE(9-1) June 2017 3H Q18] 𝐴, 𝐵
and 𝐶 are points on a circle of radius 5 cm,
centre 𝑂. 𝐷𝐴 and 𝐷𝐶 are tangents to the
circle. 𝐷𝑂 = 9 cm
Work out the length of arc 𝐴𝐵𝐶. Give your
answer correct to 3 significant figures.
The area of sector OAB is 3𝜋 𝑚 2 .
Find, in terms of 𝜋, the length of the arc
AB.
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4
Question 7
Work out the perimeter of the shaded
region. Give your answer in terms of 𝜋.
[Edexcel GCSE(9-1) Mock
Set 3 Autumn 2017 2H
Q19] The diagram shows
a sector of a circle of
radius 9 cm.
Question 10
[Edexcel GCSE Nov2015-2H Q20]
Here are two watch faces, A and B.
The sector has a
perimeter of 25 cm. Work out the value of
x. Give your answer correct to 1 decimal
place.
Question 8
[Edexcel GCSE(9-1) Nov 2017
2H Q20] 𝑂𝐴𝐶 is a sector of a
circle, centre 𝑂, radius 10 m.
𝐵𝐴 is the tangent to the circle
at point 𝐴 .𝐵𝐶 is the tangent to
the circle at point 𝐶. Angle
𝐴𝑂𝐶 = 120°
Calculate the area of the
shaded region. Give your answer correct to
3 significant figures.
Question 9
[Edexcel IGCSE(9-1) Jan2019(R)2H Q22]
Both watch faces are circular with radius 2
cm. The materials used to make both
watch faces have the same thickness. A is
made entirely of plastic. B has a 20° sector
of metal and a 340° sector of plastic.
2
The ratio of the cost per cm of the metal
2
to the cost per cm of the plastic is 3 : 2
Work out the ratio of the cost of the
materials for A to the cost of the materials
for B. Give your answer in its simplest
form. You must show
all your working.
Question 11
[Edexcel GCSE
June2007-6H Q25b
Edited] Here is the
net of a cone.
𝑂𝑃𝑄 is a sector of a circle, centre 𝑂𝑂𝐴𝐵 is
a sector of a circle, centre 𝑂. 𝐴 is the
point on 𝑂𝑃 such that 𝑂𝐴: 𝐴𝑃 = 3: 2𝐵 is
the point on 𝑂𝑄 such that 𝑂𝐵: 𝐵𝑄 = 3: 2
Angle 𝑃𝑂𝑄 = 45° . The area of the shaded
region is
81
𝜋
2
cm 2
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The net is a sector of a circle, centre O,
and radius 15 cm.
Reflex angle AOB = 216°
The net makes a cone of slant height 15
cm. Work out the vertical height of the
cone.