Container Packing (SQA National 5 Applications of Mathematics): Flashcards

The maximum number of identical boxes that will fit inside a given container.

Every box has to be aligned the same way as all the others, so the boxes cannot be turned individually to fill awkward gaps.

The completed method is:

Divide each dimension of the container by the matching dimension of the box, round each answer down to a whole number, and then multiply the three results together.

The three divisions give how many boxes fit along the height, the width and the breadth.

False.

That ignores the space left over at the end of each row, column and layer, which is wasted and cannot hold a box.

In the worked example the correct answer is 14 421 boxes, while dividing the volumes suggests over 14 700.

Because a fraction of a box will not fit.

If 22.2 boxes would reach along one side, only 22 whole boxes actually go in, and the leftover 0.2 of a box length is simply empty space.

There are two, because the height of the box is fixed by the upright condition.

Either the longer side of the box runs alongside the longer side of the container, or the shorter side of the box does.

The height still has to be divided in both cases, even though it does not change between them.

There are three.

Two of the box's dimensions are equal and the third is different, so the only real choice is which direction that odd dimension points: it can be the height, the width or the breadth.

Putting the 2.8 cm side along the 160 cm side fits more, at 14 421 boxes.

That way gives 57 and gives 11, and the height gives , so .

The other way round gives 22 and 28, and .

True.

Each orientation wastes a different amount of space at the ends of the rows, so the totals genuinely differ.

This is why every orientation the question allows has to be worked out and the largest total chosen.