For operations with uncertainty, we’ll follow two different rules depending on whether we're adding/subtracting or multiplying/dividing:
So anytime you square a measurement, add the uncertainty twice.
To convert between absolute uncertainty and percent uncertainty, we’ll use this formula (m = measurement, Δu = absolute uncertainty):
This problem gives us the maximum and minimum values for the length of a cubit. For parts (a) and (b) of the problem, we just need to convert the units from centimeters to meters, write our equation, and plug in the max and min. Part (c) is a little more complicated: we’ll need the rule for multiplying measurements with uncertainty.
We’ll assume that we know the length and diameter of the cylinder to 0.1 cubit—that is, h = 9.0 cubits and d = 2.0 cubits.
The cubit is an ancient unit of length based on the distance between the elbow and the tip of the middle finger of the measurer. Assume that the distance ranged from 43 to 53 cm, and suppose that ancient drawings indicate that a cylindrical pillar was to have a length of 9 cubits and a diameter of 2 cubits. For the stated range, what are the lower value and the upper value, respectively, for (a) the cylinder’s length in meters, (b) the cylinder’s volume in cubic meters? (c) What is the percent uncertainty in the volume?
Frequently Asked Questions
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Uncertainty concept. If you need more Uncertainty practice, you can also practice Uncertainty practice problems.
What textbook is this problem found in?
Our data indicates that this problem or a close variation was asked in Fundamentals of Physics - Halliday Calc 10th Edition. You can also practice Fundamentals of Physics - Halliday Calc 10th Edition practice problems.