Cambridge International Mathematics

6 Multi-Topic Questions (Chapter 33)

44

The diagram shows a prism of cross-sectional area 0 : 42 cm^2 and volume 7 : 56 cm^3.

a Calculate the length of the prism.

b The prism is made of wood and 1 cm^3 of this wood has a mass of 0 : 88 g. Calculate the mass of

the prism.

c The prisms are made from a block of wood of volume 0 : 5 m^3. It is known that25%of the wood

is wasted. Calculate the number of prisms which can be made, giving your answer to the nearest

thousand.

diState the area of triangle OAB.

ii What special type of triangle is triangle OAB?

iii Given that the length of AB isxcm, find an expression for the area of triangle OAB in terms

ofx. Hence find the length of AB correct to the nearest millimetre.

45

In the diagram, SR is parallel to PQ. SR=4cm, SX=2cm,

RX=3cm and PQ=7cm.

a Explain why the triangles RSX and PQX are similar.

b Calculate the length of PX and the length of QX.

c It is also given that the area of triangle RSX is 2 : 90 cm^2.

Calculate the area of triangle PQX, correct to two

significant figures.

d Use trigonometry to calculate the size of angle SRX, to

the nearest degree.

46

The main road, from A to B, through Newmarket, is straight

for 15 kilometres. The ring road, around Newmarket, is an

arc AB of a circle, centre O, of radius 12 kilometres.

aiCalculate the size of the angle markedμin the

diagram.

ii Use your answer toaito show that, correct to

three significant figures, the length of the ring road

between A and B is 16 : 2 kilometres.

b Mr Carson can drive at a steady 100 km/h along the ring

road. If he drives from A to B through Newmarket, he can average 80 km/h for 12 kilometres but

averages only 40 km/h for the 3 kilometres through the town. Calculate, to the nearest minute, the

amount of time that he saves by driving round the ring road.

O

A B

cross-section

S

R

P

Q

X

2cm

4cm

3cm

7cm

NewmarketNewmarket

15 km

12 km

AB

q

O

Adapted from June 1994, Paper 4

Adapted from June 1993, Paper 4

Adapted from Nov 1991, Paper 4

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