Colourful Cube
Age 11 to 14
Challenge Level
A colourful cube is made from little red and yellow cubes. But can you work out how many of each?
Sending a Parcel
Age 11 to 14
Challenge Level
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Changing Areas, Changing Volumes
Age 11 to 14
Challenge Level
Working on this problem will give students a deeper understanding of the relationship between volume and surface area, and how they change as the dimensions of a cuboid are altered.
Cola Can
Age 11 to 14
Challenge Level
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Cuboids
Age 11 to 14
Challenge Level
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Efficient Cutting
Age 11 to 14
Challenge Level
This problem offers an opportunity for students to apply their knowledge of areas and circumferences of circles, and volumes of cylinders.
Cuboid Challenge
Age 11 to 16
Challenge Level
This problem offers opportunities for visualising, and for consolidating the formula for working out the volume of a cuboid.
Painted Cube
Age 14 to 16
Challenge Level
Exploring a variety of painted cubes may produce patterns which students can describe spatially, numerically and algebraically.
NRICH is part of the family of activities in the Millennium Mathematics Project.