What length of steel is above the surface? (10cm diameter; 70cm height cylinder

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floating in mercury)? Situation:
A 10-cm-diameter, 70.0 cm-tall steel cylinder floats in mercury. The axis of the cylinder is perpendicular to the surface. (Density of steel: 7900kg/m^3).

What length of steel is above the surface?

Should I use a free body diagram of the cylinder to solve this problem? Can anyone help me on this?

Thank you!
 
First, you need the mass of the steel cylinder:

Volume = (10/2)*pi*70 = 1099cm3

Mass = volume*density = 1099*7.9 = 8682.1g

At room temperature, the density of Mercury is 13.5 g/cm3

Dividing the mass of the steel by the density of the mercury will tell us how much mercury needs to be displaced for the steel to float (Archimede's Principle).

8682.1/13.5 = 643.1 cm3

Now to divide that by the total volume of the cylinder to determine the proportion of the cylinder submerged by the mercury.

643.1/1099 = 0.585

Multiply this by the length to determine the length of steel submerged

0.585*70 = 41.0cm

Therefore the length of steel above the mercury is 70-41 = 29.0cm
 
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