Which of the following cubes can be made from these nets?
What is the largest cuboid you can wrap in an A3 sheet of paper?
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Investigate the number of faces you can see when you arrange three cubes in different ways.
How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?
Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have. . . .
A follow-up activity to Tiles in the Garden.
How many tiles do we need to tile these patios?
Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?