How do I calculate the mass of objects in ice?

Question

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 blocks total mass is the fossil?

I am not sure where to start, apart from calculating the volume. I don't know if I should convert the measurements to cm3 and the 21.8kg to grams?

Answer 1

I'm withdrawing my answer.

Answer 2

Let Vf = Volume of fossil

and Vi = Volume of ice

and Mf = Mass of fossil

and Mi = Mass of ice

Volume of block = 42.6*26.4*15.3 = 17,207cm³

Vf + Vi = 17207......................(1)

Mf+Mi = 21800.......................(2)

Convert mass in Equation 2 to volume via density

Vf       +         Vi = 17207.........(1)

3.64Vf + 0.917Vi = 21800........(3)

Equation 3 minus equation 1

2.64Vf - 0.083Vi = 4593 (from eq 1, Vi = 17207-Vf. Sub in Eq 3

2.64Vf -0.083(17207-Vf) = 4593

2.64Vf -1428.2 +0.083Vf = 4593

2.723Vf  = 1428.2+4593

Vf = 6021,2/2723

Vf = 2211.16cm³

Vi = 17207-2211.16 = 14995.8 cm³

Just to check:

Mass of fossil = vol * density = 2211.16 * 3.64 = 8048.6g

Mass of ice = 14995.8*0.917 = 13752g

Total 13752 + 8048 = 21800g, which is what we were given

Fossil %mass = 8048/21800*100 = 36.92%

Answer 3

yes, you should convert them.

ok first of all, calculate the volume occupied by the block:

volume = 42.6 x 26.4 x 15.3

           = 17206.992 cm^3

ok, now we can make up an equation which is basically acounting for this volume and mass: (d = m/v, so m=dv)

total mass = density(ice) x volume(ice) + density(fossil) x volume(fossil)

21800 = 0.917 x V + 3.64 x (17206.992 - V) ,-- where 'V' is volume of ice

21800 = 0.917V - 3.64V + 62633.45

-40833.45 = -2.723V

V = 14995.758 cm^3.

so the ice occupies this much space. therefore, the volume occupied by the fossil is 17206.992 - 14995.758 = 2211.234 cm^3

so, with the fossil's density as it is given, and the new found volume, we can figure out its mass:

density = mass/volume

mass = density x volume

m = 2211.234cm^3 x 3.64g/cm^3

m = 8048.89 grams

to get the perecentage of the blocks mass:

% mass of block occupied by fossil = (8048.89/21800) x 100%

= 36.92%

and there is your answer