Cambridge International Mathematics

70°

5cm

8cm

O

Q

R

P

A

C

B

D

hcm

bcm

acm

R

S

T

Q

P

()x¡+¡3 ¡cm xcm

12 cm

O

Multi-Topic Questions (Chapter 33) 657

20

On television a weather forecaster uses a cloud

symbol shown in the diagram.

Its perimeter consists of a straight line AE, two

semicircular arcs APB and DQE and the major

arc BRD of a circle, centre C.

AE=7: 5 cm, AB=DE=3cm and

BC=CD=2: 8 cm.

Angle BAE=angle DEA=70o and X is the

midpoint of BD.

aiShow that BX=2: 724 cm.

ii Calculate the angle BCX.

b Calculate

i the area of triangle BCD ii the area of the trapezium ABDE

iii the area of the major sector BCD iv the total area of the cloud symbol.

21 May/June 2000, Paper 4

The points P, Q and R lie on the circumference of a

circle, centre O. PQ=5cm, PR=8cm and angle

QPR=70o.

a Calculate the area of triangle PQR.

b

c Find the size of the obtuse angle QOR.

d Show that the radius of the circle is 4 : 18 cm,

correct to three significant figures.

e Taking the radius of the circle as 4 : 18 cm, calculate the length of the minor arc QR.

f Find the size of the reflex angle QOR.

22

a In the pyramid ABCD, ABC is the base and D is

the vertex.

Angle BCA=angle DAC=angle DAB=90o.

AD=hcm, AC=bcm and BC=acm.

(The formula for the volume of a pyramid is

1

3 base area£perpendicular height.)

i Write down a formula for the volume of the

pyramid ABCD in terms ofa,bandh.

ii Calculate the volume of pyramid ABCD when

a=6, b=5and h=8.

b The pyramid PQRST has a rectangular base with

ST=xcm and RS=(x+3)cm.

The height of the pyramid, OP, is 12 cm, where

O is the centre of the rectangle.

70° 70°

B X D

A 7.5 cm E

PQ

R

3cm

C

2.8 cm

3cm

2.8 cm

Calculate the length of the chord QR.

Adapted from Nov 2000, Paper 4

Adapted from May/June 2000, Paper 4

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Y:\HAESE\IGCSE01\IG01_33\657IGCSE01_33.CDR Friday, 14 November 2008 10:32:14 AM PETER