Victoria uses two measuring
cylinders to find the volume of a liquid. She fills the first cylinder up to
the top and then pours the rest of the liquid into the second cylinder, as shown in
the diagram. She determines that the total
volume of the liquid is 90 milliliters. Which of the following statements
explains why this answer is incorrect? a) Victoria is reading from the top of the
meniscus of the liquid in the first cylinder, rather than the bottom. b) Victoria is
reading from the bottom of the meniscus of the liquid in the first cylinder, rather
than the top. c) Victoria has not accounted for the liquid about the 50-milliliter
mark on the first cylinder. The actual volume of the liquid is
greater than 90 milliliters.
Okay, so taking a look at our
diagram, we see the two measuring cylinders: the one on the left which is filled up
to the top and the one on the right which is partially filled. In the problem statement, we’re
told that Victoria claims that the total volume of this liquid is 90
milliliters. But we’re also told that that
measurement is incorrect. These three choices a), b), and c)
are all options for explaining just why it is that that value is incorrect.
Taking a look at these choices in
order, we see that answer option a) claims that the problem is that Victoria is
reading from the top of the meniscus of the liquid in the first cylinder rather than
the bottom. Interestingly, if we look at answer
option b) then, we see that this is very similar to a). This says that the problem is that
Victoria is reading from the bottom of the meniscus of the liquid in the first
cylinder, rather than the top.
So answer options a) and b) both
boil down basically to this. One says that Victoria is reading
the volume here. But she should be reading it here,
whereas the other says the reverse.
Let’s take a look for a moment at
these two measuring cylinders. We see that the cylinders are
identical, that they both measure a maximum volume of 50 milliliters. Above that maximum level, neither
cylinder has any marks or gradations on it. When it comes to the level of the
liquid in cylinder one, this means that whether Victoria measures the level here at
the top of the meniscus or here at the bottom, in either case there won’t be a
corresponding value for the volume of that liquid. That’s because either level is
above the maximum level marked out on the cylinder, 50 milliliters.
This tells us that neither answer
option a) nor option b) can really explain why it is that her reading is
incorrect. The issue is not where she measures
the meniscus on the liquid in cylinder one, but rather it’s that the liquid in this
cylinder is above the maximum measurable value. This leads us to answer option
c). This says that Victoria has not
accounted for the liquid above the 15-milliliter mark on the first cylinder. And that’s true.
Recall that Victoria reported the
overall liquid volume as 90 milliliters. To get that, we would add together
the 50 milliliters marked out here from cylinder one to the 40 milliliters of liquid
in cylinder two. But notice that this leaves out
some of the liquid, all of the liquid above that maximum 50-milliliter mark in
Answer option c) goes on to say the
actual volume of the liquid is greater than 90 milliliters. And we see that’s true as well. The liquid volume is 90 milliliters
plus however much is contained here. So we pick answer option c) as the
accurate explanation for why it is that Victoria’s reading is incorrect, that the
liquid volume is not 90 milliliters, but rather is more.