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Convert Metric Units of Volume

In this worksheet, students will practise converting volume amounts between different units of measurements by calculating and applying a volume conversion factor.

Worksheet Overview

QUESTION 1 of 10

Converting volume units of measurement can be a challenging concept, as we need to ensure we consider volume conversion factors

 

When we are converting from, for example, metres into centimetres, we know that 1 m = 100 cm.

This leads to the misconception that 1 m3 = 100 cm3.

BUT, in reality, 1 m3 = 1,000,000 cm3.

 

Let's look at what's happening here with a diagram to help.

 

 

Looking at the volume of these two identical cubes, we can say that:

1 m × 1 m × 1 m = 100 cm × 100 cm × 100 cm

1 m3 = 1,000,000 cm3

 

 

Is there a trick here?

In a way, yes.

All we need to do for a volume conversion is to find the conversion if we were dealing with a length and then cube it to get the volume conversion factor.

 

 

Let's look at this process in action with some examples now.

 

 

e.g. Convert 1.4 m3 into cm3.

 

We know that for length, 1 m = 100 cm.

So for volume, 1 m3 = 1,000,000 cm3.

So 1.4 m3 = 1.4 × 1000000 = 14000000 cm3.

 

 

 

e.g. Convert 350 m3 into km3.

 

We know that for length, 1 km = 1000 m.

So for volume, 1 km3 = 1,000,000,000 m3.

So 350 m3 = 350 ÷ 1000000000 = 0.00000035 m3.

 

 

 

In this activity, we will convert volume amounts between different units of measurements (cm3, m3, km3) using the method shown above of calculating and applying a volume conversion factor. 

Type a number into the space to complete the sentence below. 

Type a word into the space to complete the sentence below.

Type a word into the first space and a number into the second space to complete the sentence below.

If we convert 175 cm3 into m3, what is our new equivalent volume? 

175000000 m3

0.000175 m3

1750000 m3

If we convert 4.2 km3 into m3, what is our new equivalent volume? 

42000000 m3

0.000000042 m3

4200000000 m3

State if the following conversions have been calculated correctly or not by marking each as either 'Correct' or 'Incorrect'. 

Convert 4.1 m3 into cm3.

 

You should type only numbers without a unit of measurement, as this has already been provided for you.

Convert 354 cm3 into m3.

 

You should type only numbers without a unit of measurement, as this has already been provided for you. 

Convert 4.1 km3 into m3.

 

You should type only numbers without a unit of measurement, as this has already been provided for you. 

Convert 2950000 m3 into km3.

 

You should type only numbers without a unit of measurement, as this has already been provided for you. 

  • Question 1

Type a number into the space to complete the sentence below. 

CORRECT ANSWER
EDDIE SAYS
If we compare the lengths first, we know that 100 cm = 1 m. If we cube these numbers to convert them into volumes, we reach: 100 × 100 × 100 = 1 × 1 × 1 1,000,000 cm3 = 1 m3
  • Question 2

Type a word into the space to complete the sentence below.

CORRECT ANSWER
EDDIE SAYS
Did you spot that this was the opposite operation to the statement in our previous question? So we already know that our volume conversion factor is: 100 × 100 × 100 = 1 × 1 × 1 1,000,000 cm3 = 1 m3 As we are converting from centimetres into metres this time, it may be helpful to think that centimetres are much smaller than metres so we will need to have more of them. To create more, we need to multiply by our volume conversion factor. Does that make sense?
  • Question 3

Type a word into the first space and a number into the second space to complete the sentence below.

CORRECT ANSWER
EDDIE SAYS
If we compare the lengths first, we know that 1000 m = 1 km. If we cube these numbers to convert them into volumes, we reach: 1000 × 1000 × 1000 = 1 × 1 × 1 1,000,000,000 m3 = 1 km3 As we are converting from kilometres into metres this time, it may be helpful to think that metres are much smaller than kilometres so we will need to have more of them. To create more, we need to multiply by our volume conversion factor.
  • Question 4

If we convert 175 cm3 into m3, what is our new equivalent volume? 

CORRECT ANSWER
0.000175 m3
EDDIE SAYS
Firstly, we need to calculate our volume conversion factor: 100 cm = 1 m 100 ×, 100 × 100 = 1 × 1 × 1 1,000,000 cm3 = 1 m3 As a m3 is bigger than a cm3, we need to create less of them so we must divide: 175 ÷ 1000000 = 0.000175 m3
  • Question 5

If we convert 4.2 km3 into m3, what is our new equivalent volume? 

CORRECT ANSWER
4200000000 m3
EDDIE SAYS
Let's calculate our volume conversion factor first: 1 km = 1000 m 1 × 1 × 1 = 1000 × 1000 × 1000 1 km3 = 1,000,000,000 m3 As a m3 is much smaller than a km3, we need to create more of them so we must multiply: 4.2 × 1000000000 = 4200000000 m3
  • Question 6

State if the following conversions have been calculated correctly or not by marking each as either 'Correct' or 'Incorrect'. 

CORRECT ANSWER
EDDIE SAYS
Did you remember to cube the conversion factors here? Let's work through each conversions one at a time, and see if our answer match those provided. cm3 > m3: 100 cm = 1 m so 1000000 cm3 = 1 m3 m3 are bigger than cm3 so we need to create less of them by dividing: 1500 ÷ 1000000 = 0.0015 m3 This does not match the answer provided, so the first conversion is incorrect. m3 > cm3: 1 m = 100 cm so 1 m3 = 1000000 cm3 cm3 are smaller than m3 so we need to create more of them by multiplying: 1.5 × 1000000 = 1500000 cm3 This does match the answer provided, so the second conversion is correct. km3 > m3: 1 km = 1000 m so 1 km3 = 1000000000 m3 m3 are smaller than km3 so we need to create more of them by multiplying: 1.5 × 1000000000 = 1500000000 m3 This does not match the answer provided, so the final conversion is incorrect too. Were you able to identify the one correct conversion here?
  • Question 7

Convert 4.1 m3 into cm3.

 

You should type only numbers without a unit of measurement, as this has already been provided for you.

CORRECT ANSWER
EDDIE SAYS
Remember to cube the length conversion: 1 m = 100 cm so 1 m3 = 1000000 cm3 cm3 are smaller than m3 so we need to create more of them by multiplying: 4.1 × 1000000 = 4100000 cm3
  • Question 8

Convert 354 cm3 into m3.

 

You should type only numbers without a unit of measurement, as this has already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
100 cm = 1 m so 1000000 cm3 = 1 m3 m3 are larger than cm3 so we need to create less of them by dividing: 354 ÷ 1000000 = 0.000354 m3 Well done if you quickly spotted that this was the inverse operation of the process in the previous question.
  • Question 9

Convert 4.1 km3 into m3.

 

You should type only numbers without a unit of measurement, as this has already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
Remember to cube the length conversion: 1 km = 1000 m so 1 km3 = 1000000000 m3 m3 are smaller than km3 so we need to create more of them by multiplying: 4.1 × 1000000000 = 4100000000 m3
  • Question 10

Convert 2950000 m3 into km3.

 

You should type only numbers without a unit of measurement, as this has already been provided for you. 

CORRECT ANSWER
EDDIE SAYS
1000 m = 1 km so 1000000000 m3 = 1 km3 km3 are larger than m3 so we need to create less of them by dividing: 2950000 ÷ 1000000000 = 0.0295 km3 Well done for completing this activity! You can now convert volume amounts between different units of measurement by finding the volume conversion factor and identifying whether to multiply or divide.
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