1. Suppose we need to know the volume of a cylindrical water tank. Someone else has done the diameter and height measurements of the tank and they have reported the values to us. They have told us that the height is 125.3 cm, and that diameter is 38 cm. They have not told us uncertainties, nor have they told us anything about their measurement methods. We wish to calculate the volume of the tank, with an uncertainty estimate. (a) Notice that the height is reported to more precision than the diameter. Assume that the measurer has not made any mistakes in the measurements, and that they have reported them with reasonable precision. So, in other words we are assuming that we really do know the height with more precision than the diameter. Speculate about why the height measurement might be more precise than the diameter measurement. It will be helpful to think about how you would actually go about making these two measurements, in practice. (b) Calculate the volume of the water tank and use the significant figure "rules" to round the result appropriately. (c) Without any more knowledge of the uncertainties, we are forced to make some assumptions. The typical assumption that we would make is that the uncertainties are "half of the smallest digit reported". So, under this assumption, the height has an uncertainty of 0.05 cm (so we believe that the height is between 125.25 cm and 125.35 cm), and the diameter has an uncertainty of 0.5 cm (so we believe that the diameter is between 37.5 cm and 38.5 cm). Under this assumption, calculate the minimum and maximum values that we believe the volume of the water tank could have. Don't do any rounding of these answers yet. You will do rounding in the next step. (d) Examine the minimum and maximum values of the volume that you found in the previous part of the question. Look at each digit. Which digits do we know the values of "for sure". Which digits can we narrow down to a few possible options? Which digits do we know absolutely nothing about? (e)how many significant figures should the volume have.