Cambridge International Mathematics

Similarity (Chapter 18) 379

5 Consider the followingsimilarsolids. Find the unknown length or volume:

ab

cd

6 Two solid wooden spheres have radiiacm and 3 acm respectively. If the smaller one has volume

250 cm^3 , find the volume of the larger one.

7 The surface areas of two similar cylinders are 6 cm^2 and 54 cm^2 respectively.

a If the larger cylinder has height 12 cm, find the height of the smaller one.

b If the volume of the smaller cylinder is 24 cm^3 , find the volume of the larger one.

8 Two similar cones have volumes 4 cm^3 and 108 cm^3 respectively. Find the surface area of the smaller

one if the larger has surface area 54 cm^2.

9 Two buckets are similar in shape. The smaller one is 30 cm tall and the larger

one is 45 cm tall.

Both have water in them to a depth equal to half of their heights. The volume

of water in the small bucket is 4400 cm^3.

a What is the scale factor in comparing the smaller bucket to the larger one?

b What is the volume of water in the larger bucket?

c The surface area of the water in the larger bucket is 630 cm^2. What is

the surface area of the water in the smaller bucket?

10 Two cylindrical containers have capacities 875 ml and

2240 ml respectively. Thin straws are placed in the

cylinders as shown.

These have length 10 cm and 16 cm respectively. Are

the cylinders similar? Give evidence to support your

answer.

3cm

6cm

10 cmC

VcmC 6cm

9cm

12 cmC VcmC

xcm

9cm

10 cmC

50 cmC

flat

10 cm

16 cm

11 Answer the questions of theOpening Problemon page 367.

6cm

27 cmC

64 cmC

xcm

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Y:\HAESE\IGCSE01\IG01_18\379IGCSE01_18.CDR Friday, 7 November 2008 4:34:10 PM PETER