Maths Week Scotland 2025 - Challenge 2 - Cabin bags

Mr Smith: This problem is all about dimensions and volume.

Dave is packing for flights to meetings in Dublin and Amsterdam and then back to Glasgow.

Each flight is with a different airline and each airline has different restrictions on the size of cabin bags.

Flying Glasgow to Dublin, with Heather Airlines, the maximum bag size is 56 × 45 × 20 cm,

Flying Dublin to Amsterdam, with Trefoil Airways, bags can be no bigger than 54 × 42 × 25 cm,

And flying Amsterdam to Glasgow, with Air Tulipa, the biggest bag dimensions allowed are 52 × 44 × 30 cm.

What is the volume of the largest cabin bag Dave can take on his business trip?

Explain your answer.

Pupil: You don’t need to know all the dimensions for all the flights to find your answer

Pupil: To find the maximum volume doesn’t mean using the biggest dimensions.

Pupil: You should only have to make one calculation to find the correct answer.

Good luck

Mr Smith: Did you work out the volume of the largest cabin bag allowed?

Let’s look at how we got our answer.

The bag must satisfy all the restrictions.

So it must have the smallest length of the three, the smallest width of the three and the smallest height of the three airlines’ regulations:

This gives us: length of 52 cm (Air Tulipa), width of 42 cm (Trefoil Airways), and a height of 20 cm (Heather Airlines).

And now we know the maximum dimensions of largest cabin bag allowed across the airlines, we can multiply these to find the volume.

The maximum volume is: 52 × 42 × 20 = 43680 cm cubed.

Well done if you got this speedy boarding style.