# Calculate Density

In this worksheet, students will be asked to work out densities given the mass and volume of objects.

Key stage:  KS 3

Curriculum topic:   Geometry and Measures

Curriculum subtopic:   Derive and Apply Formulae

Difficulty level:

### QUESTION 1 of 10

Density is an example of a compound measure, which is one that involves more than one unit of measurement.

Density is a measure of mass (e.g. kg, g) in relation to unit volume (e.g. m3, cm3) and can be measured in kg/m3, g/cm3 etc.

We calculate densities using the following formula:

Density = Mass ÷ Volume

Example

A large block of oak has a mass of 185 kg and a volume of 0.25 m3

Find its density in kg/m3.

Density = Mass ÷ Volume = 185 ÷ 0.25 = 740 kg/m3.

Now it's over to you to apply this formula to word problems by yourself.

A large block of walnut wood has a mass of 171 kg and a volume of 0.3 m3

Find its density in kg/m3.

(Just the number as units are given in the question.)

A rock has a mass of 1.8 kg and a volume of 72 cm3

Find its density in g/cm3.

(Just the number as units are given in the question.)

A piece of charcoal has a mass of 10.4 g and a volume of 50 cm3

Find its density in g/cm3.

A lump of butter has a mass of 250 g and a volume of 290 cm3

Find its density in g/cm3.

A litre of water has a mass of 1 kg.

Find its density in g/cm3.

(Just write the number.)

A kilogram of lead has a volume of 88.18 cm3.

Find its density in g/cm3.

(Just write the number to 2 dp.)

A toy has a mass of 250 g and a volume of 1000 cm3.

Find its density in g/cm3.

(Just write the number.)

A marble statue has a mass of 3200 kg and a volume of 1.25 m3.

Find its density in kg/m3.

(Just write the number.)

A large slab of concrete has a mass of 24 kg and a volume of 0.01 m3.

Find its density in kg/m3.

(Just write the number.)

1 kg of flour has a volume of 1700 cm3.

Find its density in g/cm3.

(Just write the number to 3 sig. figs.)

• Question 1

A large block of walnut wood has a mass of 171 kg and a volume of 0.3 m3

Find its density in kg/m3.

(Just the number as units are given in the question.)

570
EDDIE SAYS
Density = mass / volume 171 kg ÷ 0.3 m³ = 570 kg/m³ The word problem has given us both the mass and the volume. It's our job to substitute these values into the equation that gives us density.
• Question 2

A rock has a mass of 1.8 kg and a volume of 72 cm3

Find its density in g/cm3.

(Just the number as units are given in the question.)

25
EDDIE SAYS
We know that density = mass / volume We also know that 1.8 kg = 1800 g So our calculation is: 1800 ÷ 72 = 25 g/cm³ Is this beginning to get less daunting?
• Question 3

A piece of charcoal has a mass of 10.4 g and a volume of 50 cm3

Find its density in g/cm3.

0.208
EDDIE SAYS
We know that density = mass / volume We also know that 10.4 g = 50 cm³ So our calculation is: 10.4 ÷ 50 = 0.208 g/cm³
• Question 4

A lump of butter has a mass of 250 g and a volume of 290 cm3

Find its density in g/cm3.

0.862
EDDIE SAYS
We know that density = mass / volume We also know that 250 g = 290 cm³ So our calculation is: 250 ÷ 290 = 0.862 g/cm³ Keep up the great work, you're almost halfway through the activity.
• Question 5

A litre of water has a mass of 1 kg.

Find its density in g/cm3.

(Just write the number.)

1
EDDIE SAYS
We know that density = mass / volume We know that 1 kg = 1000 g And, we know that 1 litre = 1000 ml So our calculation is: 1000 ÷ 1000 = 1 g/cm³
• Question 6

A kilogram of lead has a volume of 88.18 cm3.

Find its density in g/cm3.

(Just write the number to 2 dp.)

11.34
EDDIE SAYS
We know that density = mass / volume We also know that 1 kg = 1000 g So our calculation is: 1000 ÷ 88.18 = 11.340 g/cm³ Well done if you spotted that!
• Question 7

A toy has a mass of 250 g and a volume of 1000 cm3.

Find its density in g/cm3.

(Just write the number.)

0.25
EDDIE SAYS
We know that density = mass / volume So our calculation is: 250 g ÷ 1000 = 0.25 g/cm³
• Question 8

A marble statue has a mass of 3200 kg and a volume of 1.25 m3.

Find its density in kg/m3.

(Just write the number.)

2560
EDDIE SAYS
We know that density = mass / volume Hopefully you also spotted that you don't need to convert 3200 kg into grams as the units given for your answer is kg/m³. So our calculation is 3200 ÷ 1.25 = 2560 kg/m³
• Question 9

A large slab of concrete has a mass of 24 kg and a volume of 0.01 m3.

Find its density in kg/m3.

(Just write the number.)

2400
EDDIE SAYS
We know that density = mass / volume So our calculation is: 24 ÷ 0.01 = 2400 kg/m³ This is great work! One more question to tackle, then you can take a well deserved break.
• Question 10

1 kg of flour has a volume of 1700 cm3.

Find its density in g/cm3.

(Just write the number to 3 sig. figs.)

0.588
EDDIE SAYS
We know that density = mass / volume Hopefully you also spotted that in this example you needed to convert 1 kg into grams as the units given for your answer is g/m³. So our calculation is 1000 ÷ 1700 = 0.588 kg/m³ Phew, this activity required a lot of working out. Great job, why not take a break before attempting another?
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