Question

Need help with 1.3

Hollow cylinder Dimension Mean value, Stand. Deviation, Error (stan.dev.of the Thickness Inner Diameter 76.05 Height mim 0.06 0.07 0.02 mean Logger Pro, mm 0.154 0.161 0.061 4.975 128 ts 1.1 The equation that was used to calculate volume of the Hollow cylinder is Equation: V-mh R2-r2) R-76.05/2-38.03 r-38.03-4.975-33.05 Calculations: V-t 128(38.032-33.052)-142343. 16mm3 The standard deviations of the mean for each dimension found with 1.2 the following equation Equation Calculations: Och 0.061 mmN6-0.025 ga-01 61 mm/16=0.066 On 0.154mm/46-0.063 1.3 The error propagated in the volume of the hollow cylinder using the partial derivative method will be: Equation Calculations:

Answer 1

Volume = pi (R^2 - r^2) h Inner diameter = 2r = d Outer diameter = 2r + h = d + h error in Inner diameter = 2 delta r = 2 times 0.161 = 0.322 mm error in Outer diameter = 2 delta r + delta t = 0.322 + 0.154 = 0.476 mm = 2 delta R error in height = delta h = 0.061 mm V = pi (R^2 - r^2) h taking log both sides we get log V = (log pi) + log (R^2 - r^2) + log h Taking partial derivatives of both sides we get delta V/V = delta (R^2 - r^2)/R^2 - r^2 + delta h/h delta V/V = 2 delta R + 2 delta r/R^2 - r^2 + delta h/h delta V = v { (0.322 + 0.476) 4/781.448} + V {0.061/128} = 142343.16 {0.0045613} delta V = 649.268 mm^3
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