# Unit 22 Section 5 : Density

If you were to fill boxes of the same capacity with different materials you would find some easier to lift than others. For example, a box of sand would be much heavier than a box of polystyrene beads. We say that sand is more dense than polystyrene. Density, mass and volume are connected by these relationships: Different materials have different densities.
For example, mercury has a density of 13600 kg/m³ and air has a density of 1.4 kg/m³.
An important density to remember is the density of water: it is 1000 kg/m³ or 1 g/cm³.

## Practice Questions

Work out the answers to each of these questions then click to see whether you are correct.

Practice Question 1
Calculate the mass in kilograms of 3 litres of water (remember the density of water is 1 g/cm³).

If you have the density in g/cm³ you need the the volume in cm³ and you can work out the mass in grams.
(a) What is the volume in cm³? (b) What is the mass in grams? (use mass = density × volume) (c) What is the mass in kilograms? Practice Question 2
The metal block shown below has mass 2kg. Calculate the density of the metal in g/cm³.

If you want the density in g/cm³ you need the mass in grams and the volume in cm³.
(a) What is the mass in grams? (b) What is the volume in cm³? (c) What is the density in g/cm³? Practice Question 3
A type of wood has density 0.7 grams/cm³.
A piece of this wood is 3 cm by 10 cm by 180 cm.
What is the mass of this piece of wood in grams?

If you want the mass in grams, you need the density in g/cm³ and the volume in cm³.
(a) What is the volume in cm³? (b) Which formula is needed to calculate the mass? (c) What is the mass in grams? ## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the 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 to see the answer.

Question 1
Calculate the mass of the following volumes of water:
 (a) 100 cm³ grams  (b) 2 litres grams  (c) 0.5 litres grams  Question 2
The mass of the metal block below is 3 kg. (a) What is the density of the block in kg/cm³? kg/cm³  (a) What is the density of the block in grams/cm³? grams/cm³  Question 3
A polystyrene block has dimensions 1 m by 2 m by 3 m.
The mass of the block is 24 kg.

(a) Calculate the density of the polystyrene in grams/cm³.
grams/cm³  (b) A smaller block of polystyrene has dimensions 50 cm by 20 cm by 30 cm. What is its mass?
grams  Question 4
The diagram below shows a tank that is to be filled with water. Calculate the mass of water (in kg) if the tank is to be: (b) half full kg  Question 5
A rectangular block of metal, 5 cm by 8 cm by 10 cm, has a mass of 500 grams.

Calculate the density of the metal in
 (a) g/cm³ g/cm³  (b) kg/cm³ kg/cm³  Question 6
A book has dimensions 1 cm by 24 cm by 30 cm. Its mass is 576 grams.

(a) Calculate the density of the book in g/cm³.
g/cm³  (b) What is the mass of a book with dimensions 1.5 cm by 20 cm by 15 cm?
grams  Question 7
The density of concrete is 4 grams/cm³.

(a) Calculate the mass (in kg) of a concrete block with dimensions 10 cm by 45 cm by 22 cm.
kg  (b) Calculate the volume of a concrete block with a mass of 5 kg.
cm³  Question 8
A box with dimensions 6 cm by 5 cm by 2 cm is full of soil. The mass of the soil in the box is 72 grams.

(a) Calculate the density of the soil in g/cm³.
g/cm³  (b) Calculate the mass of soil (in kg) needed to fill a window box which has dimensions 70 cm by 20 cm by 25 cm.
kg  Question 9
The density of sea water is not the same as the density of pure water.
When the tank below is filled with sea water the mass of the water is 82400 kg. (a) If the tank was filled with pure water, what would be the mass of the water? kg  (b) Does pure water or sea water have the higher density? Pure water Sea water  (c) What is the density of sea water in grams/cm³? grams/cm³  (d) What is the mass (in grams) of 1 litre of sea water? grams  Question 10
One type of metal has a density of 4 grams/cm³.
Another type has a density of 5 grams/cm³.
Pendulums weighing 500 grams are made from both types of metal.

Calculate the difference in the volume of the pendulums made from the two types of metal.
cm³  You have now completed Unit 22 Section 5
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