Surface and surface area

A follow-up activity to Tiles in the Garden.

How many tiles do we need to tile these patios?

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 choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

How much peel does an apple have?

What is the largest cuboid you can wrap in an A3 sheet of paper?

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.

What's the most efficient proportion for a 1 litre tin of paint?