1. Volume of cubes and cuboids
Mathematics
Volume of cubes and cuboids

2. Lesson Objectives The aim of this powerpoint is to help you…
to learn and use the formulas for finding the volume of a cuboid
to learn how to find the side length of a cube given the volume.

3. Dimensions REMEMBER: Perimeter is 1D (one dimension/distance)
Area is a 2D (two perpendicular dimensions multiplied together)
Volume is 3D (three perpendicular dimensions multiplied together)
ADDING distances, areas or volumes together makes longer distances, bigger areas or bigger volumes
You have to MULTIPLY dimensions or distances together to get areas or volumes

4. Measures
REMEMBER:
When calculating perimeters, areas and volumes, all dimensions must have the same type of units otherwise you will need to convert them first.
You will need to recall…
1cm = 10mm
1m = 100cm (or 1m = 1000mm)
1km = 1000m

5. Volume of Cuboids Volume is 3-dimensional.
You must multiply 3 perpendicular dimensions together.
The volume of a cuboid (or cube) is its length × width × height (or depth)
Formula: V = l × w × h
width
length
depth

6. Volume of Cuboids
Area is measured in squares – count them or calculate them but the measures are square-units.
Volume is measured in cubes – count them or calculate them but the measures are cube-units.
As area is already 2-dimensional, you can also calculate the volume of a cuboid (or cube) as the area of its end shape × height (or depth)
V = A × h
depth
area
height
area

7. Working backwards… V V V lw h l wh lh w V A h V = lwh
These formula triangles show that given the volume and any 2 dimensions, to find the third dimension you divide the volume by the product of the other two.
V = Ah
V V V
lw h l wh lh w V
A h
This formula triangle shows that given the volume and the area of one face, to find the third dimension you divide the volume by the area.

8. Special case…Cube
As a cube’s dimensions are all equal, the same distance is multiplied by itself three times, which is the definition of ‘cubing’.
V = l × l × l so V = l³
To work backwards, you do the opposite of ‘cubing’.
Therefore, if you know the volume of a cube, you can find the side-length by cube-rooting…
l = ³ V

9. Quick Practice What are the volumes of these 3D shapes? CUBE CUBOID
12mm
25cm
1.5m
20cm

10. Solutions… Volume = length × length × length CUBE CUBOID
Volume = length × width × height
CUBE
CUBOID
12mm
25cm
1.5m
20cm
Volume = 12mm × 12mm × 12mm = 1728mm³
NB. Dimensions must be the same units!
Volume = 25cm × 20cm × 150cm = 75000cm³ OR
Volume = 0.25m × 0.2m × 1.5m = 0.075m³

11. What next?
Print out the notes called PAV5a-Volume. Read through them and make sure you answer any questions.
Work through the MyMaths lesson and its online homework called Volume of Cuboids found at:
Save and complete the worksheet called Volume-S1.xlsx
Now move on to the PAV5b powerpoint