DENSITY PROBLEMS
1.
An unknown metallic substance has a mass of 276.5 g and a volume of 35 cm3.
Determine the density of the substance.
Given: Mass = 276.5g
Volume = 35cm3
(7.9 g/cm3)
Density = Mass
Volume
= 276.5g
35 cm3
= 7.9 g/cm3
Find: Density
 The density of the metallic substance is 7.9 g/cm3.
2.
A rectangular solid measures 6.0 cm x 7.5 cm x 16.0 cm and has a mass of 6400 g.
Calculate the density of the object.
Given: M = 6400g
Length = 6.0cm
Width = 7.5cm
Height = 16.0cm
First, find the Volume:
Volume = Length X Width X Height
= 6.0cm X 7.5cm X 16.0cm
= 720 cm3
Find: Density
Then find the Density:
Density = Mass
Volume
= 6400g
720cm3
= 8.9g/cm3
(8.9 g/cm3)
 The density of the rectangular solid is 8.9g/cm3.
3.
A body whose mass is 60 g is dropped into a cylinder containing 150 mL of water.
The water rises to the 200 mL mark. What is the density of the body?
(1.2 g/mL = 1.2 g/cm3)
Given: Mass = 60g
Volume of water = 150mL
Volume of water + body = 200mL
Find: Density of body
 The density of the body is 1.2g/mL.
First, find the volume of the body:
Volumebody = Volumewater + body – Volumewater
= 200mL – 150mL
= 50mL
Then, find the density of the body:
Density = Mass
Volume
= 60g
50mL
= 1.2g/mL
4.
An empty 25 mL graduated cylinder has a mass of 82.14 g. When 25.0 mL of an
unknown liquid is poured into the cylinder, the total mass of the cylinder and liquid
is 105.25 g. What is the density of the liquid?
Given: V = 25.0mL
Mcylider = 82.14g
Mtotal = 105.25g
Find: D
(0.92 g/mL)
First, find Mliquid: Mliquid = Mtotal – Mcylinder
= 105.25g – 82.14g
= 23.11g
Next, find D: D = M
V
= 23.11g
25.0mL
= 0.92g/mL
 The density of the liquid is 0.92g/mL.
5.
Calculate the density of a 400 cm3 piece of wood that has a mass of 200 g.
Given: M = 200g
V = 400cm3
Find: D
(0.5 g/cm3)
D=M
V
= 200g
400cm3
= 0.5g/cm3
 The density of the wood is 0.5g/cm3.
6.
A steel beam has a mass of 3200 kg. Its dimensions are 10 m by 0.2 m by 0.2 m.
Calculate the beam's density.
(8000 kg/m3)
Given: M = 3200kg
L = 10m
W = 0.2m
H = 0.2m
Find: D
First, find V:
V=LXWXH
= 10m X 0.2m X 0.2m
= 0.4m3
Next, find D:
D=M
V
= 3200kg
0.4m3
= 8,000kg/m3
 The density of the steel beam is 8,000kg/m3.
7.
The mass of a chunk of metal is 48.0 g. When the chunk is placed in a graduated
cylinder containing 12.0 mL of water, the level rises to 26.0 mL. Calculate the
metal's density.
Given: M = 48.0g
Vwater+chunk = 26.0mL
Vwater = 12.0mL
Find: D
(3.4 g/cm3)
First, find Vchunk:
Vchunk = Vwater+chunk – Vwater
= 26.0mL = 12.0mL
= 14.0mL
Next, find D
D=M
V
= 48.0g
14.0mL
= 3.4g/mL
1mL = 1cm3,  The density of the metal is 3.4/cm3.
8.
Rewrite the equation D = m/V to express mass by itself and volume by itself
D=M
V
9.
VxD=MxV
V
VxD=M
VxD=M
D
D
V=M
D
A piece of wood, having a density of 0.805 g/cm3, has a volume of 550 cm3.
What is the mass of the wood?
Given: D = 0.805g/cm3
V = 550cm3
(442.8 g)
M=VxD
= 550cm3 x 0.805g/cm3
= 442.8g
Find: M
 The mass of the wood is 442.8g.
10. The density of a certain grade of petroleum is 0.750 g/mL. What volume would
be occupied by 150 g of the liquid?
Given: D = 0.750g/mL
M = 150g
Find: V
V=M
D
= 150g
0.750g/mL
= 200mL
 The petroleum would occupy 200mL of space.
(200 mL)
11. A rectangular solid has dimensions of 1.8 cm by 3.5 cm by 10.0 cm and is made
of brass. Calculate the mass of the solid if brass has a density of 8.5 g/cm3.
Given: D = 8.5g/cm3
L = 1.8cm
W = 3.5cm
H = 10.0cm
Find: M
(535.5 g)
First, find V:
V=LxWxH
= 1.8cm x 3.5cm x 10.0cm
= 63.0cm3
Next, find M:
M=DxV
= 8.5g/cm3 x 63.0cm3
= 535.5g
 The solid brass weighs 53.5g.
12. A five cent piece is 2.12 cm in diameter, 0. 177 cm thick and has a density of
8.00 g/cm3. Calculate it's mass. (Volume for a cylinder = r2h)
Given: Diameter = 2.12cm
Thickness = 0.177cm
Density = 8.00g/cm3
Find: M
(5.0 g)
First, find the Volume:
Volumecylinder = r2h
= (1/2diameter)2thickness
= (1/2 2.12cm)2 0.177cm
= 3.14 x (1.06cm)2 x 0.177cm
= 3.14 x (1.12) x 0.177cm
= 0.624cm3
Next, find the Mass:
M=VxD
= 0.624cm3 x 8.00g/cm3
= 5.0g
 The five cent piece weighs 5.0g.
13. A bottle weighs 12.24 g when empty, 34.74 g when filled with water and 31.82 g
when filled with turpentine. What is the density of the turpentine?
(Re: density of water is 1.0 g/cm3)
(0.87 g/mL)
Given: Mbottle = 12.24g
First, find Vwater:
Mbottle+water = 34.74g
Vwater = Mbottle+water - Mbottle
Mturpentine+bottle = 31.82g
Dwater
3
Dwater = 1.0g/cm
= 34.74g – 12.24g
1.0g/cm3
Find: Dturpentine
= 22.5cm3
** Since the bottle is the same, the volume of the water and the volume of the turpentine must be equal.
Next, find Dturpentine:
Dturpentine = Mturpentine+bottle - Mbottle
Vwater
= 31.82g – 12.24g
22.5cm3
= 0.87g/cm3
1 cm3 = 1 mL
 The density of the turpentine is 0.87g/mL.
14. A copper cylinder has a density of 8.95 g/cm3 and a mass of 534 g.
Calculate its height if the diameter of the cylinder is 2.0 cm.
(Volume for a cylinder = r2h)
Given: D = 8.95g/cm3
M = 534g
Diameter = 2.0cm
Find: height
First, find the Volume:
V=M
D
= 534g
895g/cm3
= 59.66cm3
Next, find the height:
Volumecylinder = r2h
V
= (1/2 d)2 x h
(1/2 d)2
(1/2 d)2
V
= h
2
(1/2 d)
59.66cm3 = h
(1/2 2.0cm)2
59.66cm3
=h
2
3.14 (1)
19cm = h
 The height of the copper cylinder is 19cm.
(19 cm)