1. goteachmaths.co.uk Volume of a Cuboid – Complete Lesson
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2. 14 January 2019
Volume of a Cuboid

4. 6 faces, 8 vertices, and 12 edges.
Cube or cuboid?
5cm
6cm
7cm
6cm
5cm
6cm
A cube’s sides are all equal.
2cm
A cuboid has
6 faces, 8 vertices, and 12 edges.
8cm
4cm

5. Volume of a cuboid = Width x Height x Length
1cm
1cm
1cm
= 1cm3
3cm
Height
5cm
Length
6cm
Width
Volume of a cuboid = Width x Height x Length
= 6 x 3 x 5 = 90
cm3

6. Volume of a cuboid = Width x Height x Length
1cm
1cm
1cm
= 1cm3
3cm
Height
5cm
Length
6cm
Width
No animations.
Volume of a cuboid = Width x Height x Length
= 6 x 3 x 5 = 90
cm3

7. Volume of a Cuboid = Width x Height x Length
3cm
5cm
40mm
Volume of a Cuboid = Width x Height x Length
= 40 x 3 x 5 = 600cm3
Units must be the same!
= 4 x 3 x 5 = 60cm3

8. 7m
3cm
5cm 2m
4cm 5m
5cm
7cm
5mm
4cm
4cm
1cm
1.5cm
3cm

9. 7m 3cm 5cm 2m 4cm = 60cm3 5m = 70m3 7cm 5mm 4cm = 14cm3 = 55.5cm3 5cm

10. Volume of a Compound Cuboid
Split the shape to find the
area of the cross-section.
3cm
A: 3 x 7 = 21cm2
B: 3 x 3 = 9cm2 A
7cm
3cm
A + B = 30cm2 B
3cm
Multiply the cross-section
by the length.
4cm
6cm
Volume = 30 x 3 = 90cm3

11. Volume of a Compound Cuboid
Split the shape to find the
area of the cross-section.
3cm
A: 3 x 7 = 21cm2
B: 3 x 3 = 9cm2 A
7cm
3cm
A + B = 30cm2 B
3cm
Multiply the cross-section
by the length.
4cm
No animations.
6cm
Volume = 30 x 3 = 90cm3

12. 1d.p.
7.5cm
4cm
6cm
25mm
3.5cm
4.5cm
4cm
2cm
1cm
3cm
6cm
2cm
4cm
1cm
7cm
2cm
4cm

13. 1d.p.
7.5cm
4cm
6cm
25mm
= 84.4cm3
3.5cm
= 84cm3
4.5cm
4cm
= 72cm3
= 140cm3
2cm
1cm
3cm
6cm
2cm
4cm
1cm
7cm
2cm
4cm

14. Calculate the volume of these cuboids.
Complete the table for these cuboids. a
Cuboid
Width
Height
Length
Volume A
5cm
7cm
5.5cm B
6cm
4.5cm
189cm3 C
94.5cm3 D
8.5cm
148.75cm3 E
2.4cm
3.2cm
6.7cm b
3cm
6cm
5cm
6cm
2cm
8cm
7cm c d
5.5cm
10cm
f) These are the side lengths of cubes.
Calculate their volumes.
g) These are the volumes of cubes.
Calculate their side lengths.
3cm
8cm
5mm
3.5m
0.5cm
64cm3
125m3
343mm3
2.744cm3
This is a cube.
What is it’s volume?
8cm
2cm e
These two cuboids
are identical.
The volume of this cuboid is 105cm3.
What is the cuboid’s length?
45mm i h
50mm f
6cm
1cm
2cm
1cm g
60mm
3cm
5cm j
2.5cm
The volume of a cuboid is 64m3.
Its height is twice its width.
Its length is twice its height.
What are the cuboid’s dimensions?
5cm
6cm
2.5cm
4cm
5.5cm
2cm
3cm

15. 90cm3 84cm3 240cm3 4cm 512cm3 88cm3 5m 125mm3 7mm 42.875m3 1.4cm
Calculate the volume of these cuboids.
Complete the table for these cuboids. a
Cuboid
Width
Height
Length
Volume A
5cm
7cm
5.5cm
192.5cm3 B
6cm
4.5cm
189cm3 C
3.5cm
94.5cm3 D
8.5cm
2.5cm
148.75cm3 E
2.4cm
3.2cm
6.7cm
51.456cm3
90cm3 b
84cm3
3cm
6cm
5cm
6cm
2cm
8cm
7cm c
240cm3 d
5.5cm
10cm
f) These are the side lengths of cubes.
Calculate their volumes.
g) These are the volumes of cubes.
Calculate their side lengths.
4cm 5m
7mm
1.4cm
3cm
512cm3
125mm3
42.875m3
0.125cm3
88cm3
8cm
5mm
3.5m
0.5cm
64cm3
125m3
343mm3
2.744cm3
This is a cube.
What is it’s volume?
8cm
2cm e
These two cuboids
are identical.
216cm3
The volume of this cuboid is 105cm3.
What is the cuboid’s length?
45mm i h
50mm
16875mm3 f
6cm
1cm
2cm
1cm g
60mm
3cm
5cm j
2.5cm
The volume of a cuboid is 64m3.
Its height is twice its width.
Its length is twice its height.
What are the cuboid’s dimensions?
5cm
6cm
34.5cm3
2.5cm
7cm
4cm
5.5cm
2cm
2cm, 4cm, 8cm
102cm3
3cm

16. Check your success! I can calculate the volume of a cube.
I can calculate the volume of a cuboid.
I can calculate the volume of a compound cuboid.

17. Check your success! I can calculate the volume of a cube.
I can calculate the volume of a cuboid.
I can calculate the volume of a compound cuboid.
Optional addition.
Effort this lesson?