Page 178 - Mathematics Coursebook

18.5 Calculating the surface area of cubes and cuboids

18.5 Calculating the surface area of cubes and cuboids

!e surface area of a cube or cuboid is the total area of all its faces.

!e units of measurement for surface area are square units, for example, mm , cm or m .
2
2
2

!is cube has six faces.

!e area of one face = 2 × 2
= 4 cm 2 2 cm
!e surface area of the cube = 6 × 4 2 cm

= 24 cm 2 2 cm

!is is a net of a cuboid. It can be folded up to make the cuboid shown.

height (h)
width (w)
length (l)
You can see that the cuboid has two blue faces, two red faces and two green faces.

Area of one red face = length × width
Area of one blue face = length × height
Area of one green face = width × height

To work out the surface area you need to add together the areas of all the faces. !is cuboid has
two faces of each colour so you would need to multiply the area of each face by 2, before adding
them all together.

Worked example 18.5

Work out the surface area of this cuboid.
3 cm
5 cm
8 cm

Area of top face = 8 × 5 = 40 cm Use the formula: area = length × width
2
Area of front face = 8 × 3 = 24 cm Use the formula: area = length × height
2
Area of side face = 5 × 3 = 15 cm Use the formula: area = width × height
2
Surface area = 2 × 40 + 2 × 24 + 2 × 15 Multiply the area of each face by 2.
= 80 + 48 + 30 Add the areas to fi nd the total surface area.
= 158 cm Remember to include the units in your answer.
2
) Exercise 18.5

1 Work out the surface area of each of these cuboids.
a b c
4 cm 2 cm 2 cm

6 cm 5 cm
5 cm
9 cm 10 cm
4 cm
18 Area, perimeter and volume 177