DENSITY
The density of a material tells us the mass (in kg) of 1 m3 of the material.
𝑚
𝑚𝑎𝑠𝑠 (𝑘𝑔)
𝜌=
𝑑𝑒𝑛𝑠𝑖𝑡𝑦(𝑘𝑔⁄𝑚3 ) =
3
𝑉
𝑣𝑜𝑙𝑢𝑚𝑒 (𝑚 )
𝑚𝑎𝑠𝑠 = 𝑣𝑜𝑙𝑢𝑚𝑒 × 𝑑𝑒𝑛𝑠𝑖𝑡𝑦
𝑣𝑜𝑙𝑢𝑚𝑒 =
𝑚=𝑉×𝜌
𝑚𝑎𝑠𝑠
𝑑𝑒𝑛𝑠𝑖𝑡𝑦
𝑉=
𝑚
𝜌
WORKED EXAMPLE
QUESTION
A block of lead has a volume of 0.5 m3. Its mass is 5700 kg. What is its density?
ANSWER
Step 1: Write down what you know, and
what you want to know.
Step 2: Use the triangle to decide how to
find the answer - the density.
Step 3: Use the figures given to work out
the answer.
The density of lead is 11 400 kg/m3
m = 5700 kg
V = 0.5 m3
 =?
𝜌=
𝜌=
𝑚
𝑉
5700 𝑘𝑔
= 11400𝑘𝑔/𝑚3
0.5 𝑚3
Questions
1. A block of aluminium has a mass of 108 kg, and its volume is 0.04 m3. What is the density of
aluminium?
2. A full bucket contains 20 kg of water. What is the volume of the bucket? (Density of water =
1000 kg/m3)
3. A barometer is to be filled with 0.001 m3 of mercury. It is more accurate to weigh the mercury, rather than to measure its volume. What is the mass of this
volume of mercury? (Density of mercury = 13 600 kg/m3)
4. Copy and complete the table below.
OBJECT
MASS (kg)
VOLUME (m3)
a)
W
5000
2
b)
X
20 000
c)
Y
d)
Z
DENSITY (kg/m3)
4000
6
10 000
3000
5000
5. A supplier's catalogue offers blocks of tungsten (mass 38.6 g, volume 2 cm3), and rods of wolfram (mass 96.5 g, volume 5 cm3). Which has the greater
density, tungsten or wolfram?
In questions 6 to 10, you will have to work out the volume or mass from information given in the question.
6. What is the volume of air in a lab of dimensions 8 m x 5 m x 3 m? What is the mass of the air? (Density of air = 1.3 kg/m3)
7. A brick has dimensions 8 cm x 10 cm x 25 cm. Its mass is 3.6 kg. What is the density of the brick, in g/cm3?
8. A steel cube has sides of length 10 cm. What is its mass? (Density of steel = 7.7 g/cm3)
9. A stone has mass 80 g. When it is submerged in water in a measuring cylinder, the level rises from 120 cm3 to 160 cm3.
a. What is the volume of the stone?
b. What is its density?
10. A student is measuring the density of ethanol. She makes the following measurements: mass
of empty bottle = 28.7 g, mass of water-filled bottle = 78.7 g, mass of ethanol filled bottle =
68.7 g. If she knows that the density of water is 1 g/cm3, what is the density of ethanol?
11. How much does 1000 cm3 of water weigh? What is the mass of the same volume of mercury,
in kg? (Density of water = 1g/cm3, density of mercury = 13.6 g/cm3)
12. An apple is found to weigh 1 N. Its volume is 125 cm3 .Would it float on water?
You will need to use the fact
that 1 kg mass has a weight
of 9.8 N (9.8 newtons) on
Earth and that objects float
if their density is less than
the liquid they are in