### 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.