You may also like

problem icon

Building Tetrahedra

Can you make a tetrahedron whose faces all have the same perimeter?

problem icon

Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

problem icon

Areas and Ratios

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

Three Cubes

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2
 

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?
  •  
  •