A new mattress arrives as a rolled up vacuum sealed cyclinder. The mattress is laid out flat as shown below, but air needs to be allowed into the packaging so it inflates to its final cuboid shape. As the mattress expands, the width and length won’t change, but the depth will increase significantly. The current depth is just 15% of the final depth of the mattress.
What is the difference in the finished volume of the mattress, and the volume of the cyclinder that was delivered?
This question stretches the most able GCSE students. For those that don’t know where to start, it is always useful to remind them that marks are awarded for part of the final answer even if not completed. As no formulae are given for a question like this, the question works well to consolidate volume learning. Students take 3-4 minutes to answer this question in full.
Teachers could extend the learning by considering:
- Express the inflated volume as a percentage of the packed volume