Volume and Capacity
3.0 Measurements · 3.4 Volume and Capacity
Syllabus tag: Kenya CBC | Grade 7 Mathematics | Strand 3.0 Measurements | Sub-Strand 3.4 Volume and Capacity (8 lessons)
Lesson objectives
By the end of this topic, you will be able to:
- Identify the metre cube (m³) as a unit of volume, and convert it to and from cm³
- Work out the volume of cubes, cuboids and cylinders
- Identify the relationship between cm³, m³ and litres
- Relate volume to capacity, and work out the capacity of containers
Volume and Capacity
Volume is the space a solid takes up. Capacity is how much a container holds. They measure the same thing from two directions.
a) Cubic units
Volume uses cubic units, because three lengths are multiplied together.
A cube of side 1 cm has a volume of 1 cm³. A cube of side 1 m has a volume of 1 m³.
Since 1 m is 100 cm, 1 m³ is 100 × 100 × 100 cm³. That is 1 000 000 cm³.
That number surprises people. The unit is cubed, so the conversion factor is cubed too.
b) Volume of a cuboid
Multiply length by width by height.
All three must be in the same unit. If one is in metres and the others in centimetres, the answer is meaningless.
For a cube all three are equal, so the volume is side × side × side.
c) Volume of a cylinder
A cylinder has a circular base. Its volume is the area of that base multiplied by the height.
The base area is πr², so the volume is πr²h.
Use the radius, not the diameter. If given the diameter, halve it first.
d) Capacity
Capacity is measured in litres and millilitres.
The link to volume is fixed: 1 litre = 1 000 cm³, and 1 millilitre = 1 cm³.
So a container of volume 1 540 cm³ holds 1.54 litres.
For larger containers, 1 m³ holds 1 000 litres. A water tank of 2 m³ holds 2 000 litres.
e) Converting between units
| From | To | Do this |
|---|---|---|
| m³ | cm³ | multiply by 1 000 000 |
| cm³ | m³ | divide by 1 000 000 |
| cm³ | litres | divide by 1 000 |
| litres | cm³ | multiply by 1 000 |
| m³ | litres | multiply by 1 000 |
A check: the smaller the unit, the larger the number.
f) Where this is used
A water engineer sizes a tank. A trader sells cooking oil by the litre. A builder orders concrete by the cubic metre. A nurse measures medicine in millilitres.
Words to know
- Volume — the amount of space a solid object occupies, measured in cubic units.
- Capacity — the amount a container can hold.
- Metre cube (m³) — a unit of volume equal to the volume of a cube 1 m on each side.
- Litre — a unit of capacity equal to 1000 cm³.
:::checkpoint Check yourself
- How many cm³ are in 1 m³?
- Find the volume of a cuboid 10 cm by 6 cm by 4 cm.
- A cylinder has radius 14 cm and height 10 cm. Find its volume, taking π as 22/7.
- A container holds 3 500 cm³. What is its capacity in litres? :::
Bridge to practice
Try the exercises below — on volume of cubes, cuboids and cylinders, and converting to capacity.