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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?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
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.
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?
How many faces can you see when you arrange these three cubes in different ways?
A follow-up activity to Tiles in the Garden.
What is the largest cuboid you can wrap in an A3 sheet of paper?
Which of the following cubes can be made from these nets?
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?
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 their surface areas equal to their volumes?
Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.
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?