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'Three Cubes' printed from http://nrich.maths.org/
1. The distance between centres of two adjacent faces of a cube is $8$cm.
What is the side length of the cube?
2. 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?
3. 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?