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Broad Topics >

Coordinates and Coordinate Geometry > Coordinates - 3D

##### Age 16 to 18 Challenge Level:

Stick some cubes together to make a cuboid. Find two of the angles
by as many different methods as you can devise.

##### Age 16 to 18 Challenge Level:

A spherical balloon lies inside a wire frame. How much do you need
to deflate it to remove it from the frame if it remains a sphere?

##### Age 16 to 18 Challenge Level:

P is the midpoint of an edge of a cube and Q divides another edge
in the ratio 1 to 4. Find the ratio of the volumes of the two
pieces of the cube cut by a plane through PQ and a vertex.

##### Age 16 to 18 Challenge Level:

What is the surface area of the tetrahedron with one vertex at O
the vertex of a unit cube and the other vertices at the centres of
the faces of the cube not containing O?

##### Age 16 to 18 Challenge Level:

Find the shape and symmetries of the two pieces of this cut cube.

##### Age 16 to 18 Challenge Level:

Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.

##### Age 14 to 18 Challenge Level:

Some treasure has been hidden in a three-dimensional grid! Can you work out a strategy to find it as efficiently as possible?