Volume and Capacity Notes

3.4 Volume and Capacity

Volume

Definition

Volume is the space occupied by matter, or enclosed by a surface.
The SI unit of volume is cubic metre (m³).
Other units include cubic centimetres (cm³).

Notes

1 m³ = 1 m × 1 m × 1 m
1 m = 100 cm
1 m³ = 100 cm × 100 cm × 100 cm
1 m³ = 1 000 000 cm³

Example 3.19

Convert 100 cm³ to cubic metres.

Answer: 0.0001 m³

Example 3.20

Convert 0.2 m³ to cubic centimetres.

Answer: 200 000 cm³

Volume of Objects

The table below shows the formulae used in calculating volumes of cubes, cuboids and cylinders.

Example 3.21

Calculate the volume of a cube of side 5 cm.

Solution

Volume of cube with side 5 cm = 125 cm³

Example 3.22

Calculate the volume of the cuboid measuring 140 cm by 30 cm by 70 cm in cubic metres.

Solution

Volume of cuboid =1.4×0.3×0.7 = 0.294 m³

Example 3.23

A cylindrical tank has a diameter of 140 cm and a height of 450 cm. Calculate the volume of the tank in cubic centimetres.

Solution

The diameter is 140 cm, therefore the radius is 70 cm.

V = πr²h

V = (22/7) × 70 cm × 70 cm × 450 cm

V = 6,930,000 cm³

Capacity

Definition

Capacity is the amount of substance a container can hold.
Capacity in fluids (liquids and gases) is measured in litres.

Notes

1 litre = 1000 millilitres
1 millilitre = 1 cm³
1 litre = 1000 cm³
1000 litres = 1 m³

Example 3.24

What volume in cubic centimetres is equivalent to 2 litres?

Solution

2 litres = 2000 cm³

Example 3.25

A tank whose base is a rectangle of dimensions 2 metres by 4 metres has a height of 0.5 metres. What is the capacity of the tank in litres?

Solution

We first obtain the volume in cubic metres.

V = l × w × h

V = 4 m × 2 m × 0.5 m

V = 4 m³

We now convert the volume to capacity.

1 m³ = 1000 litres

4 m³ = x

x = (4 m³ × 1000 litres) / 1 m³

x = 4000 litres

Exercise 3.4 Interactive

Exercise 3.4

1. Convert each into cubic centimetres.

(a) 2.5 m³

(b) 0.89 m³

(d) 0.0052 m³

Multiply each value by 1 000 000 because 1 m³ = 1 000 000 cm³.

2. Convert each to cubic metres.

(a) 3500 cm³

(b) 4050 cm³

(d) 150 cm³

Divide each value by 1 000 000 because 1 m³ = 1 000 000 cm³.

3. Convert each to litres.

(a) 450 cm³

(b) 1.03 m³

(d) 150 m³

Use: 1 litre = 1000 cm³ and 1 m³ = 1000 litres.

4. Convert to cubic metres.

(a) 2000 litres

(b) 350 litres

Divide litres by 1000 because 1000 litres = 1 m³.

5. Convert to cubic centimetres.

(a) 100 litres

(b) 45 litres

(d) 10000 millilitres

1 litre = 1000 cm³ and 1 ml = 1 cm³.

6. Convert to litres.

(a) 200 ml

(b) 4000 ml

Divide millilitres by 1000.

7. Calculate the volume of a cube whose side is 6 cm.

V = s³ = 6 × 6 × 6 = 216 cm³.

8. Calculate the volume of a cylinder of radius 70 cm and height 1 m. (Answer in m³)

Convert radius: 70 cm = 0.7 m
V = πr²h = 22/7 × (0.7)² × 1 = 1.54 m³.