Volume and capacity

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

What is the largest cuboid you can wrap in an A3 sheet of paper?

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

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

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?

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

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?

This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal spoons. Each day a spoonful was used to perfume the bath of a beautiful princess. For how many days did the whole jar last? The genie's master replied: Five hundred and ninety five days. What three numbers do the genie's words granid, ozvik and vaswik stand for?

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