Answers:
(a) 
(b) Volume gold: 
, Volume cupper: 
(c) 
Explanation:
<h2>(a) Mass of gold </h2><h2 />
We are told the total mass 
of the coin, which is an alloy of gold and copper is:
(1)
Where 
is the mass of gold and 
is the mass of copper.
In addition we know it is a 22-karat gold and the relation between the number of karats 
and mass is:
(2)
Finding 
:
(3)
(4)
(5) This is the mass of gold in the coin
<h2>(b) Volume of gold and cupper</h2><h2 />
The density 
of an object is given by:
If we want to find the volume, this expression changes to: 
For gold, its volume 
will be a relation between its mass (found in (5)) and its density 
:
(6)
(7)
(8) Volume of gold in the coin
For copper, its volume 
will be a relation between its mass and its density 
:
(9)
The mass of copper can be found by isolating from (1):
(10)
Knowing the mass of gold found in (5):
(11)
Now we can find the volume of copper:
(12)
(13) Volume of copper in the coin
<h2>(c) Density of the sovereign coin</h2><h2 />
Remembering density is a relation between mass and volume, in the case of the coin the density 
will be a relation between its total mass and its total volume 
:
(14)
Knowing the total volume of the coin is:
(15)
(16)
Finally:
(17) This is the total density of the British sovereign coin
