You may also like
Wrapping Gifts
A box of size a cm by b cm by c cm is to be wrapped with a square piece of wrapping paper. Without cutting the paper what is the smallest square this can be?
Plane to See
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.
Four Points on a Cube
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:
Glue three cubes together to make a cuboid of dimensions $3$ by $1$ by $1$. Label $4$ points on the cuboid with coordinates $A = (0,0,0)$, $B=(1,1,1)$, $C=(2,1,0)$ and $D=(3,1,0)$. Now the challenge is to find at least two different ways to calculate the angles $\angle ABC$ and $\angle ABD$.
Copyright © 1997 - 2020. University of Cambridge.
All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.