Question

To calculate the volume of a cylinder, we have equation like this: V = πd 2 4 h = πr 2h d is the diameter, r is the radius and h is its height. We can measure the diameter (r = d 2 ) and height directly. To calculate the confidence interval of the volume, we should use the propagation of errors. We use the micrometer screw to measure the diameter. The minimum interval on the screw is 0.01mm. What is the confidence interval for δd and δr?

Answer 1

`\delta d =` +/- 0.01 mm

`\delta r =` +/- 0.02 mm

Explanation:

`\delta d`. The error of a quantity directly measured is the uncertainty of the tool used for measuring. So error for diameter is 0.01 mm.

`\delta r`. The error of a quantity obtained multiplying/dividing a measure by a constant is calculated multiplying/dividing the measure uncertainity by the same constant. Radius is calculated as r=2*d, so we calculate
`\delta r` multiplying the diameter uncertainty by 2 (
`\delta r = 2*0.01=0.02`).