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E4.3 Circle Problems (Area,
Circumference and Arcs)
Question Paper
Level
Subject
Exam Board
Level
Topic
IGCSE
Maths (0580)
Cambridge International Examinations (CIE)
Extended
E4. Mensuration (Perimeters, Areas and
Volumes)
E4.3 Circle Problems (Area,Circumference&Arcs)
Question Paper
Sub-Topic
Booklet
60 minutes
Time Allowed:
Score:
/ 50
Percentage:
/100
Grade Boundaries:
A*
A
B
C
D
E
U
>85%
75%
60%
45%
35%
25%
<25%
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1.
AB is an arc of a circle, centre O, radius 9 cm.
The length of the arc AB is 6 r cm.
The area of the sector AOB is kr cm2.
A
Find the value of k.
NOT TO
SCALE
O
9 cm
B
k= .................................................. [3]
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2
B
45°
20°
A
C
NOT TO
SCALE
E
D
ABCE is a cyclic quadrilateral.
AED and BCD are straight lines.
AC = CD, angle ABC = 45° and angle ACE = 20°.
Work out angle ECD.
Angle ECD = ................................................. [3]
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3
A
NOT TO
SCALE
12 cm
O
145°
B
The diagram shows a sector, centre O, and radius 12 cm.
(a) Calculate the area of the sector.
........................................... cm2 [3]
(b) The sector is made into a cone by joining OA to OB.
Calculate the volume of the cone.
1
[The volume, V, of a cone with base radius r and height h is V = rr 2 h.]
3
........................................... cm3 [6]
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4
A
O
NOT TO
SCALE
38°
25 cm
B
The diagram shows a sector of a circle, centre O, radius 25 cm.
The sector angle is 38°.
Calculate the length of the arc AB.
Give your answer correct to 4 significant figures.
AB= ............................................ cm [3]
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5
(a) The points A, B, C and D lie on a circle.
AC is a diameter of the circle.
ST is the tangent to the circle at A.
S
48°
B
27°
A
T
y°
x°
D
NOT TO
SCALE
C
Find the value of
(i)
x,
Answer(a)(i) x = ................................................. [2]
(ii)
y.
Answer(a)(ii) y = ................................................. [2]
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(b) The diagram shows a shaded shape formed by three semi-circular arcs.
The radius of each semi-circle is shown in the diagram.
NOT TO
SCALE
6 cm
4 cm
2 cm
(i) Calculate the perimeter of the shaded shape.
Answer(b)(i) ........................................... cm [2]
(ii)
The shaded shape is made from metal 1.6 mm thick.
Calculate the volume of metal used to make this shape.
Give your answer in cubic millimetres.
Answer(b)(ii) ........................................ mm3 [5]
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6
D
C
NOT TO
SCALE
O
E
48°
B
A
In the diagram, B, C, D and E lie on the circle, centre O.
AB and AD are tangents to the circle.
Angle BAD = 48°.
(a) Find
(i) angle ABD,
Answer(a)(i) Angle ABD = ................................................ [1]
(ii) angle OBD,
Answer(a)(ii) Angle OBD = ................................................ [1]
(iii) angle BCD,
Answer(a)(iii) Angle BCD = ................................................ [2]
(iv) angle BED.
Answer(a)(iv) Angle BED = ................................................ [1]
(b) The radius of the circle is 15 cm.
Calculate the area of triangle BOD.
Answer(b) ......................................... cm2 [2]
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(c) Give a reason why ABOD is a cyclic quadrilateral.
Answer(c) ............................................................................................................................................
............................................................................................................................................................. [1]
7
(a)
E
D
140°
120°
F
NOT TO
SCALE
C
A
B
In the hexagon ABCDEF, AB is parallel to ED and AF is parallel to CD.
Angle ABC = 90°, angle CDE = 140° and angle DEF = 120°.
Calculate angle EFA.
Answer(a) Angle EFA = ................................................. [4]
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(b)
D
C
30°
NOT TO
SCALE
X
100°
A
B
In the cyclic quadrilateral ABCD, angle ABC = 100° and angle BDC = 30°.
The diagonals intersect at X.
(i)
Calculate angle ACB.
Answer(b)(i) Angle ACB = ................................................. [2]
(ii)
Angle BXC = 89°.
Calculate angle CAD.
Answer(b)(ii) Angle CAD = ................................................. [2]
(iii)
Complete the statement.
Triangles AXD and BXC are ............................................................. .
[1]
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(c)
R
S
NOT TO
SCALE
Y
P
Q
P, Q, R and S lie on a circle.
PR and QS intersect at Y.
PS = 11 cm, QR = 10 cm and the area of triangle QRY = 23 cm2.
Calculate the area of triangle PYS.
Answer(c) .......................................... cm2 [2]
(d) A regular polygon has n sides.
n
degrees.
Each exterior angle is equal to
10
(i) Find the value of n.
Answer(d)(i) n = ................................................. [3]
(ii) Find the size of an interior angle of this polygon.
Answer(d)(ii) ................................................. [2]