Question

Priya is conducting a density experiment in which the density of a metal is calculated by the formula density = mass/volume. She tests six different metals with volumes between 15 and 32 cubic centimeters (1 cc3 = 1 mL) by first weighing each, and then dropping them into a graduated cylinder with 50.0 mL of water in it and recording the amount of water displaced by reading the new volume off the cylinder.

Which scenario would most likely result in the greatest percent error of the density of each metal? Assume Priya uses the same scale and graduated cylinder for each metal.

using a graduated cylinder calibrated with 10 mL intervals
using a scale with a variance of 0.0005 to weigh each metal
using a graduated cylinder calibrated with 100 mL intervals
using a scale that is completely balanced and accurate

Answer 1

Using a graduated cylinder calibrated with 100 mL intervals.

Reason: the volume measurement (displaced water) dominates the uncertainty. Your metals displace only 15–32 mL, so a cylinder with 100 mL graduations has an extremely large absolute uncertainty (on the order of ±50 mL), producing huge percent errors in volume and thus density. The scale errors given are tiny in comparison (and a perfectly balanced scale gives no error).