Volume and capacity

What size square should you cut out of each corner of a 10 × 10 grid to make the box that would hold the greatest number of cubes?

What do you think is going to happen in this video clip? Are you surprised?

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

The challenge for you is to make a string of six (or more!) graded cubes.