Question Video: Measuring Volumes Using Measuring Cylinder Physics

The diagram shows a measuring cylinder with liquid in it. What is the volume of the liquid?


Video Transcript

The diagram shows a measuring cylinder with liquid in it. What is the volume of the liquid?

Taking a look at this diagram, we see it shows us a graduated or measuring cylinder, which measures the volume of liquids in units of milliliters. We notice further that the large hash marks on the side of the cylinder are marked out in units of five milliliters. So it goes five, 10, 15, 20, and so on. To figure out the volume of the liquid in our cylinder, our first step will be to put our eye on the level of the surface of the liquid.

When we do this, we get an up-close view of this section of the cylinder. Looking closely at this part of the cylinder, we notice in our expanded view that the liquid surface curves upward. This tells us that whatever this liquid is, the glass walls of the cylinder repel it. And more than that, we know that the volume of the liquid is measured at the flat part of this curve, the flat part of the meniscus.

So the question then becomes “what does this volume correspond to?” It’s two small hash marks above the larger hash mark of 45 milliliters. To find out, we can recall that the small hash marks on our cylinder evenly divide up the volume between the large marked ones. So for example, if we were to count the number of small hash marks that appear between the 10-milliliter mark and the 15-milliliter mark, that would show us how much volume change each small hash mark corresponds to.

Let’s do that now. Let’s count the number of hash marks that appear in between these two larger labeled ones. So if we start just above 10 milliliters, we count one, two, three, four small hash marks, then five, a medium-sized one, then six, seven, eight, and then nine hash marks. And the next hash mark is the large labeled one, 15 milliliters. This means that the volume between 10 and 15 milliliters on this cylinder is divided up into 10 even volumes.

That tells us that each small hash mark corresponds to a change in volume of one-half of a milliliter. We can write it this way: we could say that Δ𝑣, the smallest measurable change in volume according to the markings on the cylinder, is equal to one-half or 0.5 milliliters. Now that we know this fact, we can go back to our up-close view and figure out which volume this second hash mark above 45 milliliters corresponds to.

Beginning at 45 milliliters, when we move up one hash mark, that means we’re now at a volume of 45.5 milliliters since each small hash mark corresponds to a volume of Δ𝑣. But we move up a second one. That means that our volume now is 46.0 milliliters. That’s the volume at the measurement of the flat part of the meniscus, the top part of its curve in this case.

So by getting our eye in the right position level with the surface of our liquid in the cylinder and then measuring at the flat part of the meniscus of the curve of the liquid, we found its volume. It’s 46.0 milliliters.

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