Density calculations: is it gold?
𝑑𝑒𝑛𝑠𝑖𝑡𝑦 =
𝑚𝑎𝑠𝑠
𝑣𝑜𝑙𝑢𝑚𝑒
ρ = m/V (ρ is the symbol for density and it is the greek letter rho, the letter after pi in the greek
alphabet)
SI unit of density: kg/m3 = kg m-3 but if you use grams and cm3 to calculate the density, state the density
in g/cm3
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎 𝑐𝑢𝑏𝑜𝑖𝑑 = 𝑙𝑒𝑛𝑔𝑡ℎ × 𝑤𝑖𝑑𝑡ℎ × ℎ𝑒𝑖𝑔ℎ𝑡
Use the equations above to calculate all the missing values in the table and then decide if each material
will float or sink in water. If it is less dense than water, it will float and if it is denser than water it will
sink. The first row has been completed already. The density of water is 1.00 g/cm3.
After you complete the table, use the experimental data on the following pages for the 4 nuggets of
“gold” to decide what they are actually made from.
material
mass
(g)
length
(cm)
width
(cm)
height
(cm)
volume
(cm3)
density
(g/cm3)
float/sink
oak
255
5
4
15
300
0.85
float
ice
465
5
10
10
500
osmium
113
2
2
1.25
paraffin wax
360
8
8
8
tin
57.5
2.5
2
2
air
1300
100
100
100
gold
4825
5
5
250
lead
454
5
2
40
basalt
1015
7
5
aluminium
10
10
10
2.7
expanded
polystyrene
copper
5
5
5
0.015
2688
2.9
8.96
Nugget number 1 – Is it gold?
Volume of nugget =
Mass of nugget =
Density of nugget =
Material of nugget is:
Nugget number 2 – Is it gold?
Volume of nugget =
Mass of nugget =
Density of nugget =
Material of nugget is:
Nugget number 3 – Is it gold?
Volume of nugget =
Mass of nugget =
Density of nugget =
Material of nugget is:
Nugget number 4 – Is it gold?
Volume of nugget =
Mass of nugget =
Density of nugget =
Material of nugget is:
Extension
Use the equation for the volume of a sphere to determine the density of these astronomical bodies. Are
they more or less dense than water?
water has a density of 1000 kg/m3
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑎 𝑠𝑝ℎ𝑒𝑟𝑒 =
4
3
3
π𝑟
object
mass (kg)
radius (m)
Earth
5.972 × 1024
6 378 000
Jupiter
1.898 × 1027
69 911 000
Saturn
5.683 × 1026
58 232 000
Sun
1.989 × 1030
696 340 000
Neutron star
2.785 x 1030
10 000
Observable
universe
1058
4.4 x 1026
Singularity at
the centre of a
black hole
7.856 x 1030
0
volume (m3)
density
(kg/m3)
more or less
dense than
water?