Cubes and cuboids

There are 81 NRICH Mathematical resources connected to Cubes and cuboids

problem

Painted purple

Age

14 to 16

Challenge level

Three faces of a $3 \times 3$ cube are painted red, and the other three are painted blue. How many of the 27 smaller cubes have at least one red and at least one blue face?

game

We have a set of four very innocent-looking cubes - each face coloured red, blue, green or white - and they have to be arranged in a row so that all of the four colours appear on each of the four long sides of the resulting cuboid.

problem

Plane to see

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.

problem

Green cube, yellow cube

Age

7 to 11

Challenge level

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 x 2 cube that is green all over AND a 2 x 2 x 2 cube that is yellow all over?

problem

Cuboid-in-a-box

Age

7 to 11

Challenge level

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

problem

28 - upward and onward

Age

7 to 11

Challenge level

Can you find ways of joining cubes together so that 28 faces are visible?

problem

Four points on a cube

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?

problem

Dicey

Age

7 to 11

Challenge level

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

problem

Cubic covering

Age

14 to 16

Challenge level

A blue cube has blue cubes glued on all of its faces. Yellow cubes are then glued onto all the visible blue facces. How many yellow cubes are needed?

problem

Crawl around the cube

Age

11 to 14

Challenge level

Weekly Problem 37 - 2010
An ant is crawling around the edges of a cube. From the description of his path, can you predict when he will return to his starting point?

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For younger learners

Cubes and cuboids

Painted purple

Instant insanity

Plane to see

Green cube, yellow cube

Cuboid-in-a-box

28 - upward and onward

Four points on a cube

Dicey

Cubic covering

Crawl around the cube