You may also like

problem icon

Qqq..cubed

It is known that the area of the largest equilateral triangular section of a cube is 140sq cm. What is the side length of the cube? The distances between the centres of two adjacent faces of another cube is 8cms. What is the side length of this cube? Another cube has an edge length of 12cm. At each vertex a tetrahedron with three mutually perpendicular edges of length 4cm is sliced away. What is the surface area and volume of the remaining solid?

problem icon

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?

problem icon

In a Spin

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

Immersion

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

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!