 # Find Mass, Density and Volume

In this worksheet, students practise finding Mass, Density and Volume. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change, Mensuration

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Units and Measurement

Difficulty level:   ### QUESTION 1 of 10

While speed, distance and time are the most common compound unit questions you will encounter, You still need to be able to find the others. The one we will focus on here is density, mass and volume.

Density is a measurement of how heavy something is for a given unit of mass. (Effectively, the denser an object is, the heavier it is.

The hardest part of completing questions about Density, Mass and Volume is remembering the formulas.

How to find the formulas.

The easiest way to do this is to memorise the formula triangle. We can then use this to find the formulas. How do we use this?

Simple, just highlight the thing you are trying to find (I've done it with a red circle) and the formula will be what's left. Example 1: Find the volume of an object that has a density of 20g/cm3 and a mass of 500 g

The first step in these calculations is always to decide what you are trying to find. For this one, we are directly asked for the volume

V = M &div; D

Now we can plug in our numbers

V = 500 &div; 20

The last question that you need to ask is what the units are. The trick here is that they are always the same as one of the other units. The density here is given in g/cm3, so our volume must be cm3.

Distance = 25 cm3.

Example 2: An object has a volume of 75 cm3 and a mass of 15g. Find the average density of the object

Once again, we need to decide which formula. Don't worry that it asks for average density, we can use the same formulas.

D = M ÷ V

Plugging in our numbers gives...

D = 15 ÷ 75 = 0.2

Our units are grams divided by cm3 , or grams divided by cm3 (remember, the units are in the question).

Density = 0.2 g/cm3

To find the Density, we divide...

An object has a mass of 7kg and a volume of 2 cm3.

Is the average density...

3.5 g/cm3

14 g/cm3

Find the average density of an object with a Mass of 9 g and a volume of 3 cm3

Don't worry about the units for this question

To find Mass, we multiply

A metal bar has a density of 10 g/cm3 and a volume of 2cm3. Is this is the mass of the bar...

5 g

20 g

What is the mass of an object that has a density of 4 kg/m3 and a volume of 3 m3

Don't worry about the units for this question.

To find the volume, we divide

A 10kg box has an average density of 4 kg/m3

Is the volume...

40 m3

2.5 m3

What is the mass for a 4kg box has an average density of 10 kg/m3

Don't worry about the units for this question

Match the Volumes with the correct Masses and Densities.

## Column B

4 m3
25kg, 10kg/m3
2.5 m3
40kg, 10kg/m3
6 m3
12kg, 10kg/m3
1.2 m3
3kg, 0.5kg/m3
• Question 1

To find the Density, we divide...

EDDIE SAYS
Just remember, we need to look at the formula triangle and look at what's left. If I cover up density, I get mass divided by volume
• Question 2

An object has a mass of 7kg and a volume of 2 cm3.

Is the average density...

3.5 g/cm3
EDDIE SAYS
It's all about the formulas. Density = mass ÷ volume So we just have to substitute our numbers in to get 7 ÷ 2
• Question 3

Find the average density of an object with a Mass of 9 g and a volume of 3 cm3

Don't worry about the units for this question

3
EDDIE SAYS
Using the formula again Density = Mass ÷ Volume Density = 9 ÷ 3
• Question 4

To find Mass, we multiply

EDDIE SAYS
Just remember, we need to look at the formula triangle and look at what's left. If I cover up mass, I get volume multiplied by time
• Question 5

A metal bar has a density of 10 g/cm3 and a volume of 2cm3. Is this is the mass of the bar...

20 g
EDDIE SAYS
It's all about the formulas. Mass = Density x Volume So we just have to substitute our numbers in to get 10 x 2
• Question 6

What is the mass of an object that has a density of 4 kg/m3 and a volume of 3 m3

Don't worry about the units for this question.

12
EDDIE SAYS
Using the formula again Mass = Density x Volume Distance = 4 x 3
• Question 7

To find the volume, we divide

EDDIE SAYS
Just remember, we need to look at the formula triangle and look at what's left. If I cover up time, I get mass divided by density
• Question 8

A 10kg box has an average density of 4 kg/m3

Is the volume...

40 m3
EDDIE SAYS
It's all about the formulas. Volume = Mass ÷ Density So we just have to substitute our numbers in to get 10 ÷ 4
• Question 9

What is the mass for a 4kg box has an average density of 10 kg/m3

Don't worry about the units for this question

0.4
EDDIE SAYS
Using the formula again Volume = Mass ÷ Volume Time = 4 ÷ 10
• Question 10

Match the Volumes with the correct Masses and Densities.

## Column B

4 m3
40kg, 10kg/m3
2.5 m3
25kg, 10kg/m3
6 m3
3kg, 0.5kg/m3
1.2 m3
12kg, 10kg/m3
EDDIE SAYS
A couple of these are really easy, it's just a divide after all. The one that catches out the unwary is the divide by 0.5. Remember that dividing by 0.5 is exactly the same as multiply by 2.
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