You may also like

problem icon

Plane to See

P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.

problem icon

Four Points on a Cube

What is the surface area of the tetrahedron with one vertex at O the vertex of a unit cube and the other vertices at the centres of the faces of the cube not containing O?

problem icon

Instant Insanity

We have a set of four very innocent-looking cubes - each face coloured red, blue, green or white - and they have to be arranged in a row so that all of the four colours appear on each of the four long sides of the resulting cuboid.

Classic Cube

Stage: 5 Challenge Level: Challenge Level:1

Ignore any tabs.

You may like to use a dynamic geometry package or a spreadsheet program to help you. But how will you then convince me that the volume you have found is greatest?