Volume and capacity

Can you work out the dimensions of the three cubes?

Various solids are lowered into a beaker of water. How does the water level rise in each case?

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

Which of these infinitely deep vessels will eventually full up?