Question

The radius (r) and the height (h) of a cylindrical silo are measured as r=8 m and h=60 m with standard deviations of Sr = 0.01m and Sh = 0.007m, respectively. A surveyor uses these measurements to calculate the volume of the silo. What is the standard deviation of the calculated volume? Provide your answer in cubic metres rounded to the nearest 1mm^3

Answer 1

V = π R^2 H

dV = π (2 R H dR + R^2 dH) deviation of volume

dV = π (2 * 8 * 60 * .01 + 8^2 * .007) standard deviation of volume

dV = π (9.6 + .448) m^2 = 3.14 * 10.0 m^3 = 31.4 m^3

dV = 31.4 m^3

Note V = π R^2 H = V = π * 8^2 * 60 = 12060 m^3

dV / V = .0026