Cambridge International Mathematics

Mensuration (solids and containers) (Chapter 11) 249

5 Laura buys a 1 kg packet of flour. Her rectangular canister is 12 cm by 10 cm by 15 cm high. If flour

weighs 0 : 53 grams per cm^3 , will the flour fit in the canister?

6 A cubic centimetre of liquid has mass 1 : 05 grams. Calculate, in kilograms, the mass of 1 litre of liquid.

7 A rectangular block of metal measures 40 cm by 20 cm by 20 cm. It has a density of 4 : 5 g/cm^3.

Calculate the mass of the block in kilograms.

We can find the surface area and volume of more complicated solids by separating the shape into objects

that we are familiar with.

Example 14 Self Tutor

The diagram consists of a cone joined to a

cylinder.

Find, in terms of¼:

a the surface area of the solid

b the volume of the solid.

a l^2 =6^2 +8^2 fPythagorasg

) l^2 = 100

) l=10

Total area=area of cone+area of cylinder+area of base

=¼rl+2¼rh+¼r^2

=¼£ 6 £10 + 2¼£ 6 £10 +¼£ 62

=60¼+ 120¼+36¼

= 216¼cm^2

b Volume=volume of cone+volume of cylinder

=^13 ¼r^2 hcone+¼r^2 hcyl

=^13 £¼£ 62 £8+¼£ 62 £ 10

=96¼+ 360¼

= 456¼cm^3

E COMPOUND SOLIDS [6.5]

8cm

10 cm

12 cm

8cm

6cm

lcm

IGCSE01

cyan magenta yellow black

(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_11\249IGCSE01_11.CDR Tuesday, 14 October 2008 2:56:41 PM PETER