We\'re given measurements of mass (with uncertainty in grams), height (with unce

Question

We're given measurements of mass (with uncertainty in grams), height (with uncertainty in cm), and average diameter (with uncertainty in cm) of an Al cylinder as made by six different groups in a lab experiment.

 

It then asks us to use the data to find the volume and it's uncertainty in cubic centimeters and density in grams per cubic centimeter. How would I go about doing this for each of the six groups? My answers are consistantly wrong. It tells us to do it in Excel, but no matter what my answes are or how I got them, they are always wrong.

   

Group Number    Mass (g)    Height (cm)    Average Diameter (cm) 1   65.17 ± 0.05   6.41 ± 0.003   3.806 ± 0.003 2   54.43 ± 0.05   7.68 ± 0.003   3.174 ± 0.005 3   72.27 ± 0.05   10.19 ± 0.003   3.173 ± 0.003 4   104.6 ± 0.05   10.3 ± 0.003   3.820 ± 0.005 5   42.23 ± 0.05   5.91 ± 0.003   3.255 ± 0.003 6   91.5 ± 0.05   9.05 ± 0.003   3.803 ± 0.005

Explanation / Answer

I'll do it for one..

Volume V= 2*pi*r*h

Uncertainity in V = V = 2*pi* (r+ r)(h+h)- 2*pi*r*h

= 2*pi* r h + 2*pi * r*h + 2pi r h (The third term ( second order) can be neglected)

V/V= r/r + h/h (kind of like derivatives)

density = m/V

/ = m/m + V/V (even in case of denominators, the uncertanity is added to consider the worst case scenario)

for dataset 1

V= 2*pi* r* h= 2*pi* 1.903 * 6.41 = 76.60 cm^3

V/V = r/r + h/h = (0.0015)/1.903 + (0.003)/6.41 = .0012

So, V= 0.0012*76.60=0.096 cm^3

and

/= 0.05/65.17 + 0.0012

= 0.00196

=m/V= 65.17/76.6=0.85

=0.0012*.85=0.001

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