How Volume, Capacity and Mass Are Linked

15 min

Let's begin

A full yellow jerrycan holds 20 litres. Anyone who has carried one home from the water tap knows it is heavy. Just how heavy? Water follows a neat rule that links its volume, its capacity and its mass. Once you know the rule, you can say how heavy a jerrycan, a bucket or even a whole water tank is without a scale.

The water rule

You already know that 1 cm³ of space holds 1 mL. Here is the new fact: 1 mL of pure water has a mass of 1 g. Put the two together:

Volume	Capacity	Mass of that much water
1 cm³	1 mL	1 g
1 dm³ = 1 000 cm³	1 L = 1 000 mL	1 kg = 1 000 g
1 m³ = 1 000 dm³	1 000 L	1 000 kg = 1 t

This is not an accident. When scientists invented the metric system, they chose the kilogram so that 1 litre of pure water would have a mass of 1 kg. Real water from a tap is very slightly different, but in all your maths work you use: 1 L of water = 1 kg.

It only works for water

Other liquids have different masses. 1 L of cooking oil has a mass of only about 0.9 kg, which is why oil floats on water. 1 L of honey is heavier, about 1.4 kg. So never use the water rule for oil, milk or honey unless the question tells you to.

Worked examples

1. The jerrycan. 20 L of water has a mass of 20 kg. If the empty jerrycan has a mass of 1 kg, the full one is 20 + 1 = 21 kg.

2. A fish tank. A tank is 50 cm long, 30 cm wide and 40 cm high.
Volume = 50 × 30 × 40 = 60 000 cm³.
Capacity = 60 000 mL = 60 000 ÷ 1 000 = 60 L.
Mass of the water when full = 60 kg.

3. A water tank. A cuboid tank is 2 m long, 1.5 m wide and 1 m high.
Volume = 2 × 1.5 × 1 = 3 m³.
Capacity = 3 × 1 000 = 3 000 L.
Mass of the water = 3 000 kg = 3 t.

4. Going backwards. Some water has a mass of 750 g. What space does it fill? 750 g of water is 750 mL, which fills 750 cm³.

Tip

For water only, the number stays the same while the units change together: 1 cm³ → 1 mL → 1 g, and 1 dm³ → 1 L → 1 kg.

✦

Try it yourself

What is the mass of 5 L of water?
A small box holds 250 cm³ of water. What is the capacity in mL, and the mass of the water?
A tank is 1 m long, 1 m wide and 2 m high. How many litres does it hold?
3.5 kg of water fills how many cm³?
Does 1 L of cooking oil have a mass of exactly 1 kg?

Answers

5 kg.
250 mL, and the water has a mass of 250 g.
1 × 1 × 2 = 2 m³ = 2 000 L.
3.5 kg = 3 500 g of water = 3 500 mL = 3 500 cm³.
No. The rule is for water. 1 L of oil is lighter, about 0.9 kg.

Quick check

What is the mass of 12 L of water?

What you learned today

For water: 1 cm³ = 1 mL = 1 g and 1 dm³ = 1 L = 1 kg.
1 m³ holds 1 000 L of water, which has a mass of 1 tonne.
The rule is for water only; other liquids are lighter or heavier.

Sources and credits

The text of this lesson (the link between the volume, capacity and mass of water). Written by Ganzaa.
Image: Boy Carrying a Jerrycan of Water.jpg, by Ainomugisha Brendah, via Wikimedia Commons, CC BY-SA 4.0.

This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1The water rule

2It only works for water

Worked examples

Try it yourself

The water rule

It only works for water