Cambridge International Mathematics

Similarity (Chapter 18) 381

8 P and Q are markers on the banks of a canal which has parallel

sides. R and S are telegraph poles which are directly opposite

each other. PQ=30m and QR= 100m.

When I walked 20 m from P directly away from the bank, I

reached a point T such that T, Q and S lined up. How wide is

the canal?

9 The surface areas of two solid similar cones are 4 : 2 m^2

and 67 : 2 m^2 respectively.

a Find the scale factorkto enlarge the smaller cone into the larger cone.

b If the larger cone has a height of 3 : 96 m, find the height of the smaller cone.

c If the larger cone has a volume of 32 m^3 , find the volume of the smaller one.

Review set 18B

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1 Draw two quadrilaterals which have sides in proportion but are not similar.

2 Two solids are similar and the ratio of their volumes is 343 : 125.

a What is the scale factor?

b What is the ratio of their surface areas?

3 In the following figures, establish that a pair of similar triangles exists and hence findx:

abc

4 A conical flask has height 15 cm and

base diameter 12 cm. Water is poured

into the flask to a depth of 8 cm.

a Show that triangles ABC and MNC

are similar.

b Hence, show thatx=3: 2.

c Find the diameter of the surface

of the water.

5 Findxfor these similar figures:

ab

S R

P T

Q

20 m

100 m

30 m

xcm

5cm

3cm

8cm

A

B C

D E

xcm

5cm

10 cm

8cm

X

Y

Z

U V

q

q

4cm 6cm

8cm

xcm

a

a

P

Q

T S R

12 cm

8cm

15 cm

12 cmX

27 cmX

xcm

6cm

8cm 9cm

30 cmC xcmC

8cm

15 cm

A 6cm B

N

M

C

xcm

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y:\HAESE\IGCSE01\IG01_18\381IGCSE01_18.CDR Thursday, 23 October 2008 10:56:20 AM PETER