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.
A follow-up activity to Tiles in the Garden.
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?
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?
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?
An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
Can you work out the dimensions of the three cubes?
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 paper.
