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Three Cubes

Can you work out the dimensions of the three cubes?

Concrete Calculation

The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to make the concrete raft for the foundations?

In a Spin

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

Tubular Stand

Age 14 to 16
Challenge Level

The corners of the stand have to be considered and this means that each individual section is not a cylinder. However a little careful manipulation will reveal that the problem is far from insurmountable.

For the generalisation it might help to reduce the number of variables you work with to two at a time...

What is the relationship between the length and the volume if the radius is fixed?

Is there a way you can represent the relationship without just trying to describe it in words?