Unit 22 Section 4 : Capacity

When we refer to how much liquid a tank or container can hold, we often talk about its capacity in litres.
This is another way of describing its volume.

The main units of capacity are the litre (l) and the millilitre (l).
We will see how these relate to the main volume units which are the cubic centimeter (cm) and the cubic metre (m).

1 ml = 1cm
and
1 litre = 1000 ml
so
1 litre = 1000 cm

Example Question

What is the capacity, in litres, of a cubic tank with dimensions 1m by 1m by 1m?

It is always easier to convert between volume and capacity in cm³ and ml, so we work out the volume in cm³.
Each side of the tank is 1m which is 100cm, so the volume is 100cm × 100cm × 100cm = 1000000 cm³.
Every 1cm³ is equal to 1ml, so the capacity of the tank in millilitres is 1000000ml.
Every 1000ml is 1 litre, so the number of litres is 1000000 ÷ 1000 = 1000 litres.

The capacity of the tank is 1000 litres.

Because the volume of the tank in this example is 1 m³, this actually gives us another helpful fact linking volume and capacity:

1 m³ = 1000 litres

You can use the key facts in the boxes above to answer all the questions in this section.

 

Practice Questions

Work out the answers to each of these questions then click Click on this button below to see the correct answer to see whether you are correct.

Practice Question 1
A tank measures 3m by 4m by 2m. What is the capacity of the tank in litres?

We could answer this in a similar way to the example above:
What are the dimensions of the tank in centimetres?

What is the volume of the tank in cm³?

What is the capacity of the tank in millilitres?

What is the capacity of the tank in litres?

We could also answer this question using the fact that 1 m³ = 1000 litres:
What is the volume of the tank in m³?

What is the capacity of the tank in litres?

Practice Question 2
Calculate the capacity in litres of a bottle with volume 700 cm³

This time we convert to millilitres first and then to litres:
What is the capacity in millilitres?

What is the capacity in litres?

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on Click on this button to see the correct answer to see the answer.

Question 1
Convert these capacities into volumes in cm³:
(a) 2 litres cm³
(b) 5 litres cm³
(c) 0.5 litres cm³
(d) 0.2 litres     cm³
(e) 1.5 litres cm³
(f) 2.7 litres cm³
Question 2
Convert these volumes into capacities in litres:
(a) 3000 cm³ litres
(b) 7000 cm³ litres
(c) 10000 cm³     litres
(d) 750 cm³ litres
(e) 250 cm³ litres
(f) 4900 cm³ litres
Question 3
A tank has dimensions 3 m by 3 m by 2 m.

Calculate:
(a) the volume in cubic metres
(b) the capacity in litres litres

Question 4
A tank holds 5000 litres.

Calculate the volume of the tank in m³.

Question 5
Look at the three tanks below:

Which has the greatest capacity?

Question 6
A large bottle holds 2 litres of lemonade.
The lemonade is poured out into glasses that each hold 25cm³.

How many glasses can be filled?
glasses

Question 7
The diagram below shows 2 different tanks:

(a) Which tank has the greater capacity?

(b) How many more litres does the larger tank hold than the smaller one?
litres

 


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Produced by A.J. Reynolds May 2011