But a scale is not available... So the diameter of the cylindrical stainless steel rod is measured with a micrometer that is accurate to the tenths decimal place. The rod is 75 cm long with a measured diameter of 3.4 cm (therefore +or- .1cm). Stainless steel has a density of 7.8 g/cm^3.
~Volume of Cylinder: V=pi r^2h (r=radius, h=height)
~Diameter of Circle: d=2 pi (r=radius of circle)
~Mass of Object: M=V*D (V=Volume, D=Density)

A) Calculate the mass of the rod using the measure 3.4 cm diameter.
B) Write a formula that calculates mass as a function of diameter assuming a fixed density of 7.8 g/cm^3 and length of 75cm.
C) Given that the diameter's differential is .1cm, calculate the mass differential.
D) Use differentials to estimate the relative error in the mass of the steel rod with a measured diameter of 3.4cm.
E) Using differentials, for any diameter, compare the relative error in the mass compared to the relative error in the diameter.

I've done the work, but I'm not sure it is right so if you could show me your work it would be awesome so I get my homework right.

Um... the other way round is the policy of the forum, that is, you post your work and we check it for you.