Volume and Capacity for Numeracy Test Questions

You’d be forgiven for thinking that examiners had an obsession with putting things in boxes. The two things numeracy tests often ask about the capacity of boxes (in other words, how much they hold) are:

  1. The volume of the box (roughly, how much liquid you could fit in it).

  2. How many objects of a given size fit in it.

In numeracy tests, you usually measure volume and capacity in either millilitres (ml) or centimetres cubed (cm3) – they’re actually two different ways of saying the same size.

You may also see litres (1000ml) or metres cubed (m3), which work out to be the same as 1000 litres or 1,000,000cm3.

Working out the volume of a box is very straightforward:

  1. Work out the three dimensions – the height, width and depth of the box – make sure they’re all in the same units (usually centimetres).

  2. Multiply the height by the width, and the result by the depth. That’s your answer – if you measured everything in centimetres, your answer is in cm3; if everything was in metres, your answer would be in m3.

It doesn’t matter which order you multiply the three dimensions in (because the volume doesn’t change if you rotate the box), so feel free to change the order if you can come up with an easy sum first!

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Working out how many boxes fit into a bigger box is a slightly trickier problem. You’ll normally be given something like the figure, showing the dimensions of a big box and a smaller box – luckily, the smaller box will be facing in the direction you’ll be packing it (so you don’t need to worry about twisting it around).

If you’ve ever moved house, you’ll know that you can fit more cuboids – boxes or books – into a big box if you twist some of them around. As far as numeracy tests go, you can safely ignore this strategy – the question just asks about packing boxes in a boring fixed orientation.

Here are the steps:

  1. Work out how many small boxes fit along the front of the bigger box. Divide the width of the big box by the width of the smaller box. If the number doesn’t go exactly, you round down, no matter how close you are to the higher number. Write this number down.

  2. Work out how many boxes fit along the side. Divide the depth of the big box by the depth of the smaller box. Again, round down if it doesn’t go exactly. Write this number down as well.

  3. Work out how many boxes fit the height. Divide the height of the bigger box by the height of the smaller box. Once more, round down if you need to, and write the number down.

  4. Multiply your answers from Steps 1, 2 and 3. This is the number of boxes that will fit in the big box.

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