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## 'Qqq..cubed' printed from http://nrich.maths.org/

The distance between centres of two adjacent faces of a cube is
$8$cm. What is the side length of the cube?

I can make an equilateral triangle by cutting off the corner of
a cube. If the area of the largest
equilateral triangle I can create in this way is $140$cm$^2$, what
is the side length of this cube?

A third cube has an edge length of $12$cm. At each vertex, a
tetrahedron with three mutually perpendicular edges of length $4$cm
is cut away. Can you find the volume and the surface area of the
remaining solid?