Elizabeth uses a measuring cylinder to find the volume of a liquid. What value does she find?
Taking a look at this measuring cylinder, we see that it measures volume in units of milliliters. And it goes from five up to 50 milliliters in increments of five. But actually, the resolution of this measuring cylinder is better than that because we see there’re also small hash marks that are in between the larger ones marked out with numbers.
In order to find out the measurement resolution of this cylinder, let’s count the number of small hash marks that appear between two adjacent large ones. Let’s say we start at 40 milliliters at that hash mark. And we go up to 45. So counting the small hash marks that appear between these two larger ones, we count one, two, three, four, five. The fifth one is a medium-sized hash mark. Then, six, seven, eight, and nine. And in the next step is the 45-milliliter hash.
We’re finding then that there’re 10 equal divisions between the 40- and 45-milliliter marks on this cylinder. This means that each single small hash mark that we advanced corresponds to an increase in 0.5 milliliters of fluid. Put another way, we could write that Δ𝑣, which is the smallest measurable difference in volume according to this measuring cylinder, is equal to one-half or 0.5 milliliters.
This information will come in handy as we bring our eye down to the level of the fluid in this cylinder. When we look carefully at this part of the cylinder, from the expanded view, we see we have a concave meniscus. That means our liquid has the property that it’s attracted to the glass sides of our cylinder. Following the rule of measuring the volume of a liquid at the flat part of the meniscus, we see that we’ll correspond to this level on our cylinder. In other words, it’s one, two, three, four small hash marks up from this large hash mark, which indicates a volume of 30 milliliters.
We found earlier that each one of these small hash mark advancements corresponds to a change in volume of 0.5 milliliters. So starting at the large hash mark of 30 milliliters, we go up one hash mark at 30.5 milliliters, and the next one 31 milliliters. The next one is 31.5.
And the next one, the level of the flat part of our meniscus, is 32 milliliters. And that is our answer for the volume of the liquid that Elizabeth finds.