1. Surface area of cuboids
Tuesday, 12 June 2018
Surface area of cuboids
Starter
48 x 6 = x 5 =
29 x 8 = x 7 =
56 x 3 = x 4 =
67 x 2 = x 9 =
89 x 9 = x 8 =

2. Lesson Objective
By the end of the lesson I should be able to
Find the surface area of prisms
GRADE C
By the end of the lesson I
Must Calculate the area of 2d shapes
Should Calculate the surface area of cuboids
Could Calculate the surface area of triangular prisms

3. Surface area of a cuboid
To find the surface area of a shape, we calculate the total area of all of the faces.
A cuboid has 6 faces.
The top and the bottom of the cuboid have the same area.
Discuss the meaning of surface area. The important thing to remember is that although surface area is found for three-dimensional shapes, it only has two dimensions. It is therefore measured in square units.

4. Surface area of a cuboid
To find the surface area of a shape, we calculate the total area of all of the faces.
A cuboid has 6 faces.
The front and the back of the cuboid have the same area.

5. Surface area of a cuboid
To find the surface area of a shape, we calculate the total area of all of the faces.
A cuboid has 6 faces.
The left hand side and the right hand side of the cuboid have the same area.

6. Surface area of a cuboid
To find the surface area of a shape, we calculate the total area of all of the faces.
Can you work out the surface area of this cuboid?
5 cm
8 cm
The area of the top = 8 × 5
= 40 cm2
7 cm
The area of the front = 7 × 5
= 35 cm2
The area of the side = 7 × 8
= 56 cm2

7. Surface area of a cuboid
To find the surface area of a shape, we calculate the total area of all of the faces.
So the total surface area =
5 cm
8 cm
2 × 40 cm2
Top and bottom
7 cm
+ 2 × 35 cm2
Front and back
Stress the importance of working systematically when finding the surface area to ensure that no faces have been left out.
We can also work out the surface area of a cuboid by drawing its net (see slide 51). This may be easier for some pupils because they would be able to see every face rather than visualizing it.
+ 2 × 56 cm2
Left and right side
= = 262 cm2

8. Formula for the surface area of a cuboid
We can find the formula for the surface area of a cuboid as follows.
Surface area of a cuboid = h l w
2 × lw
Top and bottom
+ 2 × hw
Front and back
Pupils should write this formula down.
+ 2 × lh
Left and right side
= 2lw + 2hw + 2lh

9. How can we find the surface area of a cube of length x?
All six faces of a cube have the same area. x
The area of each face is x × x = x2
Therefore,
Ask pupils to use this formula to find the surface area of a cube of side length 5 cm.
6 × 52 = 6 × 25 = 150 cm2.
Repeat for other numbers.
As a more challenging question tell pupils that a cube has a surface area of 96 cm2. Ask them how we could work out its side length using inverse operations.
Surface area of a cube = 6x2

10. Surface area =Total area of all faces of a 3D shape
A cuboid is made up of 3 pairs of
rectangles – 6 faces
front = back
Top = bottom
Side = side

11. height
width
length
(length x height) x 2
(height x width) x 2
(length x width) x 2

12. 5cm
3cm
10cm
5 x 10 = 50 x 2 = 100
10 x 3 = 30 x 2 = 60
5 x 3 = 15 x 2 = 30
190

13. Find the surface area of these cuboids
88cm³
4cm
2cm
6cm
142cm³
7cm
3cm
5cm
220cm³
5cm
4cm
10cm
92cm³
3cm
2cm
8cm

14. 108cm²
94cm²
104cm²
24m²
150m²
96m²
340m²
88mm²
184mm²

15. Prisms

16. Surface area of a prism Here is the net of a triangular prism.
What is its surface area?
We can work out the area of each face and write it in the diagram of the net.
10 cm
12 cm
13 cm
20 cm
260 60
200 60
Explain that it is often easiest to find the surface area of a prism by first drawing its net.
In this example, we work out the area of the triangular faces using ½bh. The area of the rectangular faces are found by multiplying their length by their width.
Stress that the surface area is written in cm2. Ask pupils how this could be converted to m2 if required (by dividing by 10000).
Total surface area
260 =
= 840 cm2

19. 468mm²
300m²
1008m²
1848m²

20. 250.6cm² 4cm 4cm 50.3 cm² 25cm 6cm 150cm² 6cm 4cm 50.3 cm²
Circumference of circle = ∏ x 8 =
25 cm
Area of rectangle = 25 x 6 =
150cm²
Area of circle = ∏ x 4² =
50.3 cm²
SURFACE AREA OF CYLINDER = =
250.6cm²