Cambridge International Mathematics

232 Mensuration (solids and containers) (Chapter 11)

To help find the surface area of a solid, it is often helpful to draw anet. This is a two-dimensional plan

which can be folded to construct the solid.

Software that demonstratesnetscan be found at

Example 1

Find the total surface area of the

rectangular box:

A 1 =4£3=12cm^2 (bottom and top)

A 2 =4£2=8cm^2 (front and back)

A 3 =2£3=6cm^2 (sides)

) total surface area=2£A 1 +2£A 2 +2£A 3

=2£12 + 2£8+2£ 6

=52cm^2

So, the total surface area of the box is 52 cm^2.

Example 2

What is the total surface

area of this wedge?

We draw a net of the solid:

We next findhusing Pythagoras:

h^2 =12^2 +5^2

) h^2 = 169

) h=

p

169 = 13 fas h> 0 g

Now, A 1 =^12 bh

=^12 £ 12 £ 5

=30cm^2

A 2 =7£ 5

=35cm^2

A 3 =12£ 7

=84cm^2

A 4 =13£ 7

=91cm^2

Self Tutor

Self Tutor

http://www.peda.com/poly/

Sometimes we need

to use Pythagoras’

theorem to find a

missing length.

4cm

4cm

3cm

3cm

2cm

2cm

A 1

A 2

A 3

2cm

4cm

3cm

12 cm

5cm

7cm

7cm

12 cm

5cm A 1

A 2 A 3 A 4

A 1

hcm

hcm

) total surface area=2£A 1 +A 2 +A 3 +A 4

=2£30 + 35 + 84 + 91

= 270cm^2

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Y:\HAESE\IGCSE01\IG01_11\232IGCSE01_11.CDR Tuesday, 11 November 2008 4:37:39 PM TROY