How to find the uncertainty in a volume measurement of a cylinder?

To find the uncertainty in a volume measurement of a cylinder, you need to consider the uncertainties in the measurements of its dimensions.

Firstly, measure the diameter and height of the cylinder using a ruler or vernier caliper. Take multiple measurements and calculate the average value to reduce random errors. It's important to understand the fundamental physical quantities involved in such measurements.

Next, use the formula V = πr²h to calculate the volume, where r is the radius (half of the diameter). Calculate the volume for each set of measurements and find the average value.

To find the uncertainty in the volume measurement, you need to consider the uncertainties in the measurements of the dimensions. The uncertainty in the diameter and height measurements can be estimated by taking the range of values obtained from multiple measurements and dividing it by 2√3. This gives the standard deviation of the measurements. Understand the distinction between precision and accuracy in these measurements.

Then, use the formula for the uncertainty in the volume measurement: δV/V = 2δr/r + δh/h. Substitute the values obtained for the uncertainties in diameter and height measurements to calculate the uncertainty in the volume measurement. Familiarise yourself with the concepts of absolute and relative uncertainty to more effectively communicate the results.

Finally, report the volume measurement with its uncertainty, for example, V = (25.0 ± 0.5) cm³. This means that the true value of the volume lies within the range of 24.5 cm³ to 25.5 cm³ with 95% confidence. Always consider systematic and random errors which might influence the precision and accuracy of your measurements.

A-Level Physics Tutor Summary: To calculate the uncertainty in a cylinder's volume, first find the average measurements of its diameter and height. Then, calculate the volume and its uncertainty using specific formulas that factor in these measurements' uncertainties. Finally, present your volume with its uncertainty, indicating the most accurate value range. This method helps ensure your volume estimate is reliable and scientifically sound.