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.
Investigate the area of 'slices' cut off this cube of cheese. What
would happen if you had different-sized block of cheese to start
Investigate the number of faces you can see when you arrange three cubes in different ways.
How many tiles do we need to tile these patios?
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?
Choose a box and work out the smallest rectangle of paper needed to
wrap it so that it is completely covered.
A follow-up activity to Tiles in the Garden.
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?
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 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?
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .
At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .
What is the shape and dimensions of a box that will contain six cups and have as small a surface area as possible.
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. . . .