Calculating the mass of objects in ICE

[smarties]

Homework Statement

A rectangular block of ice containing a fossil measures 426mm x 264mm x 153mm with a total mass of 21.8kg

Density of ice = 0.917g/cm3

Density of Fossil = 3.64g/cm3

What percentage of the block's mass is the fossil?

Homework Equations

Density = Mass/Volume
Mass = Density x Volume
Volume = Mass/Density

The Attempt at a Solution

Now I calculated the volume 17206992 but I thought that was too big so I changed the measurements to cm = 42.6cm x 26.4 x 15.3 V= 17207cm3

Now this is were it gets a bit hairy I calculate the Mass

M = Density x Volume = 0.917g/cm3 x 17207cm3 = 15778.81g = 15.77kg (ICE)

M = Density x Volume = 3.64g/cm3 x 17207cm3 = 62633.48g = 62.63kg (FOSSIL)

What have I done wrong here? I am not sure of the correct steps?

 

[Dick]

You know volume(fossil)+volume(ice)=total volume. Also density(fossil)*volume(fossil)+density(ice)*volume(ice)=total mass. That's two simultaneous equations in two unknowns. Solve for the two unknown volumes.

 

[smarties]

What about if take the 21.8kg convert it to grams 21800g minus the total mass of ice 15778g

Will that mean 21800-15778 = 6022g is the mass of the Fossil ? Surely it can't be that simple? Have I missed a step ?