full coverage: arcs & sectors

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"Full Coverage": Arcs & Sectors

This worksheet is designed to cover one question of each type seen in past papers, for each

GCSE Higher Tier topic. This worksheet was automatically generated by the DrFrostMaths

Homework Platform: students can practice this set of questions interactively by going to

www.drfrostmaths.com/homework, logging on, Practise → Past Papers/Worksheets (or Library

→ Past/Past Papers for teachers), and using the ‘Revision’ tab.

Question 1 Categorisation: Determine the area of a sector.

[Edexcel IGCSE June2010-4H Q17]

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

.......................... 𝑐𝑚2

Question 2 Categorisation: Determine the length of an arc.

[Edexcel GCSE June2006-6H

Q22a]

The diagram shows a sector OABC

of a circle with centre O.

OA = OC = 10.4 cm.

Angle AOC = 120°

Calculate the length of the arc ABC of the sector.

Give your answer correct to 3 significant figures.

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

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Question 3 Categorisation: Determine a perimeter involving multiple arcs.

[Edexcel GCSE June2016-2H Q22]

OAB is a sector of a circle, centre

O. OCD is a sector of a circle,

centre O.

OCA and ODB are straight lines.

Angle AOB = 75°

OD = 6 cm DB = 4 cm

Calculate the perimeter of the

shaded region. Give your answer correct to 3 significant figures.

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

Question 4 Categorisation: Give a sector area of arc length in terms of 𝝅.

[Edexcel GCSE Nov2006-5H Q18]

OAB is a sector of a circle, centre O. Angle AOB = 60° . OA = OB = 12 cm.

Work out the length of the arc AB. Give your answer in terms of 𝜋 .

..........................


Question 5 Categorisation: Determine an angle given the area of the sector.

[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 .

𝑥 = .......................... °

Question 6 Categorisation: As before, but where an arc length or perimeter is given.

[Edexcel GCSE(9-1) Mock Set 3 Autumn 2017 2H Q19]

The diagram shows a sector of a circle of radius 9 cm.

The sector has a perimeter of 25 cm. Work out the value of x.

Give your answer correct to 1 decimal place.

𝑥 = .......................... °


Question 7 Categorisation: Determine a composite area involving a sector.

[Edexcel IGCSE Jan2017(R)-3H Q21]

The shape OABC is made

from a triangle and a

sector of a circle.

OAB is a triangle. OBC is a

sector of a circle, centre O.

OA = 12 cm AB = 16 cm

Angle OAB = 60°

Angle BOC = 38°

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

.......................... 𝑐𝑚2

Question 8 Categorisation: Determine the area of a sector given an arc length.

[Edexcel IGCSE Jan2017-3H Q22]

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.

.......................... 𝑐𝑚2


Question 9 Categorisation: Determine the area of a segment.

[Edexcel IGCSE May2012-3H Q19]

The diagram shows a sector OAPB of a circle, centre O.

AB is a chord of the circle. OA = OB = 5.4 cm. Angle AOB = 72°

Calculate the area of the shaded segment APB.

Give your answer correct to 3 significant figures.

.......................... 𝑐𝑚2

Question 10 Categorisation: Use sector/segment area in the context of percentages.

[Edexcel GCSE(9-1) Mock Set 1 Autumn 2016 - 2H Q15]

𝐴𝐵 is a chord of a circle centre 𝑂 .

The radius of the circle is 30 cm.

Angle 𝐴𝑂𝐵 = 80°

Work out what percentage of the area of the circle is shaded.

.......................... %


Question 11 Categorisation: Find a segment area in the context of circle theorems.


AOD is a diameter of a circle, with

centre O and radius 9 cm.

ABC is an arc of the circle. AC is a

chord. Angle ADC = 35°

Calculate the area of the shaded

segment. Give your answer correct

to 3 significant figures.

.......................... 𝑐𝑚2

Question 12 Categorisation: Determine the perimeter of a segment given the sector area.


The diagram shows a sector OAPB of a circle, centre O.

AB is a chord of the circle. OA = OB =

6 cm. The area of sector OAPB is 5𝜋

cm2.

Calculate the perimeter of the

shaded segment. Give your answer

correct to 3 significant figures.

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


Question 13 Categorisation: Solve applied problems involving combined sectors with different

properties, e.g. density/cost.

[Edexcel GCSE Nov2015-2H Q20]

Here are two watch faces, A and B.

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. The ratio of the cost per cm2 of the metal to the cost per cm2 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 14 Categorisation: Solve problems involving the curved surface area (i.e. a sector) of a

cone.

[Edexcel GCSE June2007-6H Q25b Edited]

Here is the net of a cone.

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.

(b) Work out the vertical height of the cone

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


Answers

Question 1

1480 𝑐𝑚2

Question 2

any value in the range 21.7 cm to 21.8 cm

Question 3

any value in the range 28.9 cm to 28.95

cm

Question 4

4𝜋

Question 5

𝑥 = 280 °

Question 6

any value in the range 𝑥 = 44.5 ° to 𝑥 =

44.6 °

Question 7

152 𝑐𝑚2

Question 8

19.8 𝑐𝑚2

Question 9

any value in the range 4.45 𝑐𝑚2 to 4.46

𝑐𝑚2

Question 10

any value in the range 6.5 % to 6.6 %

Question 11

11.4 𝑐𝑚2

Question 12

any value in the range 10.2 cm to 10.31

cm

Question 13

36: 37

Question 14

12 cm

full coverage: arcs & sectors

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