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Cut Cube

Find the shape and symmetries of the two pieces of this cut cube.

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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.

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Mesh

A spherical balloon lies inside a wire frame. How much do you need to deflate it to remove it from the frame if it remains a sphere?

Four Points on a Cube

Age 16 to 18 Challenge Level:

Take a cube of side length one unit. A vertex of the cube and the centres of the three faces not containing that vertex form the vertices of a tetrahedron. What is the surface area of this tetrahedron?

Cube with tetrahedron inside.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
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