Archimedes Principle and Specific Gravity Determination

[wildtron]

Homework Statement

a crown that is supposed to be pure gold has a mass of 850g. Its apparent mass when immersed in water is 798g. (a) what is the volume of the crown? (b)is it pure gold?If not, what is the percentage by volume of gold in the crown assuming that the crown is an alloy of lead and gold?

Homework Equations

density = m/v
specific gravity = weight of object in air /weight of object in air - weight of object immersed in water
density of gold = 19300kg/m^3
density of lead = 11300kg/m^3

The Attempt at a Solution

converted 850g to kg. 850g/1000g=.85kg
converted .85kg to weight. .85*9.8m/s^2=8.33 Newton
converted 798g to kg. 798g/1000g = .798kg
converter 798kg to weight. .798*9.8m/s^2=7.8204
used specific gravity
sp gr= 8.33N/8.33N - 7.8204N
cancel Newton
16.34615
since specific gravity is numerically equal to 1g/cm^3 in cgs system
16.34615*1g/cm^3 = 16.34615g/cm^3

converted 16.34615g/cm^3 to kg/m^3

16.34615g/cm^3 = 16346.15kg/m^3

density of crown = 16346.15kg/m^3

i don't know what's next...
i don't even know if I'm on the right track...

 

[mgb_phys]

I think you are making it a little unnecessarily complicated.

The difference in weight is equal to the mas sof water it displaces.
So it weighs the equivalent of 850-798g of water
And water has a density of 1g/cc, so it has a volume of how many cc ?