Volume and capacity

A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?

Can you draw the height-time chart as this complicated vessel fills with water?

If you had 36 cubes, what different cuboids could you make?

What fraction of the volume of this can is filled with lemonade?

Which of these infinitely deep vessels will eventually full up?

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?

An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?

If the radius of the tubing used to make this stand is r cm, what is the volume of tubing used?

Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.