The volume of a cylinder is V space equals space pi space r squared space h, where r is the radius of the circular faces and h is the height of the cylinder. Your measurements show that the mean value of r is 21 cm and its statistical and instrumental uncertainties turned out to be 0.10 cm and 0.20 cm, respectively. Likewise, that of h are 13 cm for the mean, 0.2 cm (statistical) and 0.3 cm (instrumental) for its uncertainties. A. What can you say about which source of uncertainty has the largest contribution to the overall uncertainty of V ?
B. What would you need to do to improve (reduce) the uncertainty on your calculation of V?

a) variable that introduces more uncertainty is the measurement of heigh

Explanation:

a) Uncertainty can be calculated by making differential days of volume

         V = π r² h

    the error absolute is

         ΔV = dV/dr  Δr + dV/dh   Δh

         ΔV = π h 2r Δr + π r² Δh

  to calculate the absolute error we use the instrument error

         ΔV = π 13 2 21 0.20 + π 21² 0.3

         ΔV = 343 + 415 = 758 cm³

         ΔV = 8 10² cm³

To see more clearly what measurement should be performed, look for the relative error

         ΔV / V = 2 Δr / r + Δh / h

let's use the uncertainties of the intrumetos

          ΔV/ V = 2 0.2 / 21 + 0.3 / 13

          ΔV / V = 0.019 + 0.023

let's use statistical uncertainty

          ΔV / V = 2 0.1 / 21 + 0.2 / 13

           ΔV / V = 0.0095 + 0.015

We see that the variable that introduces more uncertainty is the measurement of height, either with the uncertainty of the instrument if a single measurement is made or with the statistical uncertainty if several measurements are made.

b) To improve the precision of the medicines we must measure the height of the cylinder with more pressure, using an intricate that has less error.