Video: Measuring Volumes Using a Measuring Cylinder

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 mL. 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 above the 50 mL mark on the first cylinder. The actual volume of the liquid is greater than 90 mL.

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Video Transcript

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 cylinder one.

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.

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