Jeff buys a large cuboid-shaped container and 105 small cups. Jeff fills the large container with lemonade. He then sets up a lemonade stand and uses the large container to dispense the lemonade into the cups. At the end of the day, Jeff finds that 40 percent of the lemonade remains in the large container. All of the cups have been used. Work out the mean volume of lemonade, in centimetres cubed, that was dispensed into each cup during the day. Assume each cup was used exactly once.
When you see a question like this, it could be quite daunting because it has lots of information and it’s worth a lot of marks. I always recommend that actually you plan out what you’re going to do and work out each stage before you actually start to attempt this type of question. So this particular question splits itself up nicely into three parts. First of all, find the volume of the large container. Then, calculate the volume of lemonade that was actually used in the day. And then finally, calculate the volume per cup. As splitting it up in this way in your mind makes it easier to tackle.
So first of all, we’re gonna complete step one which is to actually find the volume of the large container. And to do that, we use the formula that tells us that the volume of a cuboid is equal to the length times the width times the height. So we’re actually gonna multiply each three of the measurements we have together. So that’s 60 multiplied by 35 multiplied by 20. And this is gonna give us an answer of 42000. And then, it’s gonna be centimetres cubed. And it’s centimeters cubed because each of our measurements were in centimetres and we multiply them all together. And also, that’s good because that’s how it wants us to work out the mean volume of our lemonade in each cup later on in the question. Okay, that’s part one complete.
So to answer part two, what we need to do is calculate the volume of lemonade that was used throughout the day. Well, Jeff finds that 40 percent of the lemonade remains at the end of the day. So therefore, we can say that 100 percent minus 40 percent equals 60 percent. So we know that 60 percent of the lemonade, or 60 percent of the volume of the container, was actually used throughout the day. So therefore, we can say 60 percent of 42000 is going to be found by 60 divided by 100 multiplied by 42000. And this is because we divide by 100 to find one percent and then multiply by 60 to find 60 percent. And this gives us an answer of 25200 and again centimetres cubed. So great, that’s part two completed.
It’s worth mentioning at this point, when we did 60 over 100 multiplied by 42000, we could have done 0.6 multiplied by 42000. And that’s because 60 percent is the same as 0.6. And that’s because 60 divided by 100 is the same as six-tenths which is 0.6. Okay, so now let’s move on to part three.
So for part three, what we need to do is actually work out the mean volume per cup. And to work this out, what we’re going to do is actually divide the total volume of lemonade dispensed, which is what we found in part two which was 25200. And then, we’re gonna divide this by 105 because that is the number of cups or the number of small cups that we have. And when we do this calculation, we get 240. And then it’s gonna be centimetres cubed because these are the units that we’ve used throughout. And we’ve now completed part three and actually answered the question. So we can say that the mean volume per cup is 240 centimetres cubed.