Compute the weight in n of a steel shaft ,35 mm diameter ,675 mm long. the
density of steel is 7680 kg/ m3.
i know i have to convert the units to cm and find volume and csa and mass but i dont think im getting the right answer. im coming up with 498.5kg

That's very interesting.  I come up with the same digits as you do, but my
decimal point is in a different place.  So, as far as you went, you did a lot
of things right.

Also, notice that the question wants the weight in Newtons, but you've
expressed your answer in kg. That's a mass,not a weight.

Since I can't look over your work, I can't show you where your mistake is. 
I guess that means that I have to go all through it . . . I have to show you
mine without ever seeing yours, and when I'm done, I get 5 points.  I am
truly psyched for the challenge !

The shaft is a long steel cylinder.
The volume of a cylinder is            V = π (radius)² (length)
Diameter = 35 mm = 0.035 meter
Radius = 17.5 mm = 0.0175 meter
Length = 675mm = 0.675 meter

Volume = π (0.0175)² (0.675) cubic meters
(about 0.00065 m³)

Mass = (Volume) x (density) = ( π x (0.0175)² x 0.675 x 7,680 ) kilograms
(about 4.987 kg)

Weight = (mass) x (gravity) = ( π x (0.0175)² x 0.675 x 7,680 ) x (9.81) =

       about  48.93 Newtons.  (almost exactly 11 pounds)

If you used ' 10 ' for the acceleration of gravity,
then the weight would be about  49.87 Newtons.

If you stopped at mass (kg) then you're off by a factor of 100 .
If you used the mass to find the weight, then you're off by a factor of 10 .

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