Calculating the mass of objects in ICE

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To find the percentage of the block's mass that is the fossil, first, the total volume of the ice block is calculated as 17207 cm³. The mass of the ice is determined using its density, resulting in 15.77 kg. The mass of the fossil is calculated using its density, yielding an incorrect value of 62.63 kg. The correct approach involves setting up simultaneous equations for the total mass and volume, leading to the conclusion that the fossil's mass can be found by subtracting the mass of the ice from the total mass of the block. This results in the fossil's mass being approximately 6.02 kg, confirming the calculations align with the principles of density and mass.
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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?
 
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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.
 
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 ?
 

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