And what is the average value of the depth, in cm? Trial Depth (cm) 1 28cm 2 32 cm 3 30 cm 4 33 cm What is the random uncertainty on the depth measurement, in cm? What is the smallest rectangular volume, in m3, that your friend could stand up in (using the average values of width, depth, and height)? Take care to round to the appropriate number of significant figures.The Weakest Link Rule We're not done. This calculated volume is based on measurements that have uncertainty. That means this volume has uncertainty too. We need to determine it so we can represent how precise our calculation is. While there are more precise and sophisticated algorithms for calculating uncertainty when you combine measured quantities (and we'll learn some in this course), when one of the measured quantities is less accurate than the others, this is done with reasonable accuracy using the weakest link rule. Here's how: 1. Determine percent uncertainties: For each quantity used in calculating the volume convert its uncertainty to a percent. This is done by dividing the uncertainty (the i value) by the average. By converting to percentages the uncertainties can be meaningfully compared to one another. Match the percent uncertainties below. percent uncertainty width [ Choose] V percent uncertainty depth [ Choose] V v' [Choose] 3.85% 1.66% 3.51% percent uncertainty height Question 10 The Weakest Link Rule (cont) 1. Identify the weakest link: The uncertainty in the width, depth, and height all contribute to the uncertainty in the volume, but one of them contributes the most. This is the weakest link, and in this case it's the depth. It has the highest percent uncertainty of all the measurements. 2. Determine the uncertainty in the calculated quantity: This is done by applying the weakest link's (the depth's) percent uncertainty to the calculated quantity (the volume). Now we're done! The smallest rectangular volume your friend could stand up in is: 0.292 m3, and the random uncertainty on that value is (in m3)