Cambridge International Mathematics

Multi-Topic Questions (Chapter 33) 655

15 Nov 2004, Paper 4

Water flows through a pipe into an empty cylindrical tank. The tank has a radius of 40 cm and a height

of 110 cm.

a Calculate the volume of the tank.

b The pipe has a cross-sectional area of 1 : 6 cm^2. The water comes out of the pipe at a speed of

14 cm/s. How long does it take to fill the tank? Give your answer in hours and minutes, correct

to the nearest minute.

c All the water from the tank is added to a pond which has a surface area of 70 m^2. Work out the

increase in depth of water in the pond. Give your answer in millimetres, correct to the nearest

millimetre.

16

a During a soccer match a player runs from A to B and

then from B to C as shown in the diagram.

AB=40m, BC=45m and AC=70m.

i Show by calculation that angle BAC=37o,

correct to the nearest degree.

ii The bearing of C from A is 051 o. Find the

bearing of B from A.

iii Calculate the area of triangle ABC.

b x- andy-axes are shown in the diagram.

¡!

AC=

³

p

q

́

, wherepandqare measured in metres.

i Show that p=54: 4. ii Find the value ofq.

c Another player is standing at D. BC=45m, angle BCD=54o and angle DBC=32o. Calculate

the length of BD.

17 May 2005, Paper 4

a Calculate the volume of the pencil.

(The volume,V, of a cone of radiusr

and heighthis given by V=^13 ¼r^2 h.)

Twelve of these pencils just fit into a rectangular box of length 18 cm, widthwcm and height

xcm. The pencils are in 2 rows of 6 as shown in the diagram.

i Write down the values ofwandx. ii Calculate the volume of the box.

iii Calculate the percentage of the volume of the box occupied by the pencils.

c Showing all your working, calculate

i the slant height,l, of the cone,

51°51°

32°32°

54°54°

North

A

B

C

D

40 m

45 m

70 m

East

1.5 cm

0.7 cm h

l

16.5 cm

wcm

xcm

18 cm

The diagram shows a pencil of length cm. It

is made from a cylinder and a cone. The cylinder

has cm and length cm. The

cone has cm and length cm.

18

07 165

07 15

diameter

diameter

::

::

b

Adapted from Nov 2004, Paper 4

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Y:\HAESE\IGCSE01\IG01_33\655IGCSE01_33.CDR Friday, 14 November 2008 10:28:29 AM PETER