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Submitted by Anonymous (not verified) on Tue, 09/08/2009 - 14:14

An eperimenter places a piece of solid metal weighing 270 g. into a graduated cyliner, which she then fills with liquid mercury. After weighing the cylinder and its contents, she remove the solid metal and fills the cylinder with mercury. Shen now finds that the cylinder and its contents weigh 116 grams less than before. The density of mercury is 13.6g/cm^3. What is the density of the solid metal?    If someone could help me with this, i have tried to work it out but my answer seems to come out wrong.

I have an answer of 23.84 g/cm3, Is this anythinhg like the correct answer? I will show you how if it is right.

Let the volume of Hg with the metal be x cm3 and the volume of Hg without the metal be y cm3
As Density = mass/volume, mass = density x volume

1st situation
Total mass = mass of cylinder + 13.6x + 270g = z grams

When 13.6x is the mass of the mercury (13.6 multiplied by its volume)

2nd situation
Total mass = mass of cylinder + 13.6y = z - 116g

Mass of cylinder + 13.6y + 116g = z grams

Linking the two equations (as they both = z)

mass of cylinder + 13.6y + 116g = mass of cylinder + 13.6x + 270g

This simplifies to
13.6y - 13.6x = 154g

So the difference in the mass of mercury between the two experiment = 154g
This calculates as there being 11.32 cm3 of mercury less in the cylinder when the metal is in there.

(Volume of mercury = mass/density = 154/13.6)

I reckon this means the metal must have a volume the same as the mercury = 11.32 cm3 as this is the reason for there being less mercury in the first situation.

So density of the metal = 270/11.32 = 23.84 g/cm3