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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?


Age 14 to 16 Challenge Level:

All objects will eventually displace the same volume of fluid.

What are the key features of each solid? What will happen to the curve as these are immersed?
There is no need for lots of algebra in order to match the curves!