The diagram shows a measuring cylinder with a liquid in it. What is the volume of the liquid?
Okay so to answer this question, we first notice that we’ve got a measuring cylinder that measures in milliliters. And secondly, we can see that a liquid has been filled up properly from the bottom all the way to somewhere in this region here. Now when we’re measuring the volume of the liquid, we need to remember that our volume measurement needs to be made at the bottom of the liquids meniscus. Now the meniscus is the curve in the top of the liquid; we can see that it’s not flat. So when we’re measuring the volume, it needs to be at the bottom of the meniscus; that’s this point here.
In other words then, our volume measurement is equivalent to this mark on the measuring cylinder. Now that mark is one, two, three small graduations away from the big line that represents 40 milliliters. So does this mean that our reading is 43 milliliters? Well no, we need to be really careful here because we can see that on our measuring cylinder we’ve got large graduations every five milliliters. This one represents 20, and this one represents 25. And in between the large graduations, we’ve got one, two, three, four, five, six, seven, eight, nine small graduations. So each small graduation does not represent one milliliter.
Now in order to work out what each small graduation represents, let’s first zoom into the diagram slightly. So here’s a zoomed-in version of our cylinder with the 20-milliliter mark and 25-milliliter mark here. Now we can see that there are one, two, three, four, five, six, seven, eight, and nine small graduations as we said earlier. Now these nine graduations actually divide up the distance between the 20-milliliter mark and the 25-milliliter mark into 10 equal segments. Look, one, two, three, four, five, six, seven, eight, nine, and 10. Therefore each graduation is going to represent a tenth of the distance between the 20-milliliter mark and the 25-milliliter mark. Now the volume represented by this distance, the distance between the 20-milliliter mark and the 25-milliliter mark, is simply given by 25 minus 20, or in other words five milliliters.
So filling a liquid up from here to here increases the volume of the liquid by five milliliters. And therefore each little graduation is going to be representing a tenth of that. So we divide five milliliters by 10. And when we do that we get 0.5 milliliters or half a milliliter. So this line represents the liquid being filled up to 20 milliliters. This very first our graduation represents 20 and half milliliters. The next one represents 21 milliliters, then 21 and half, 22, 22 and half, 23, 23 and half, 24, 24 and half, and 25 millimeters. So at this point, we know enough to come back to our actual measurement. We saw that the liquid was one, two, three little graduations above the 40-milliliter mark. So we know that the liquid is 40 milliliters plus three little graduations, where each graduation represents 0.5 milliliters. So because we’ve got three little graduations, each graduation is 0.5 milliliters, we say three times 0.5. And a bit in the parentheses ends up being 1.5 milliliters. So our total volume for the liquid is 40 plus 1.5 milliliters, which is 41.5 milliliters, and that is our final answer to the question.