### There are 14 results

Broad Topics >

3D Geometry, Shape and Space > Cubes

##### Age 16 to 18 Challenge Level:

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.

##### Age 16 to 18 Challenge Level:

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?

##### Age 16 to 18 Challenge Level:

The net of a cube is to be cut from a sheet of card 100 cm square.
What is the maximum volume cube that can be made from a single
piece of card?

##### Age 14 to 16 Challenge Level:

Can you work out the dimensions of the three cubes?

##### Age 16 to 18 Challenge Level:

This problem provides training in visualisation and representation
of 3D shapes. You will need to imagine rotating cubes, squashing
cubes and even superimposing cubes!

##### Age 14 to 16 Challenge Level:

There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being
visible at any one time. Is it possible to reorganise these cubes
so that by dipping the large cube into a pot of paint three times
you. . . .

##### Age 7 to 16 Challenge Level:

Which of the following cubes can be made from these nets?

##### Age 14 to 16 Challenge Level:

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

##### Age 14 to 18 Challenge Level:

This is an interactive net of a Rubik's cube. Twists of the 3D cube become mixes of the squares on the 2D net. Have a play and see how many scrambles you can undo!

##### Age 11 to 16 Challenge Level:

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

##### Age 16 to 18 Challenge Level:

In this problem we see how many pieces we can cut a cube of cheese
into using a limited number of slices. How many pieces will you be
able to make?

##### Age 7 to 16

A description of how to make the five Platonic solids out of paper.

##### Age 11 to 16 Challenge Level:

Toni Beardon has chosen this article introducing a rich area for
practical exploration and discovery in 3D geometry

##### Age 14 to 16 Challenge Level:

There are thirteen axes of rotational symmetry of a unit cube. Describe them all. What is the average length of the parts of the axes of symmetry which lie inside the cube?